메뉴 건너뛰기




Volumn 41, Issue 1, 1995, Pages 107-129

Spherical Codes Generated by Binary Partitions of Symmetric Pointsets

Author keywords

generalized code concatenation; set partitioning; Spherical codes

Indexed keywords

CODES (SYMBOLS); INFORMATION THEORY; SET THEORY;

EID: 0029231566     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.370114     Document Type: Article
Times cited : (36)

References (102)
  • 1
    • 0001541486 scopus 로고    scopus 로고
    • Uniqueness of certain spherical codes
    • E. Bannai and N. J. A. Sloane, “Uniqueness of certain spherical codes,” Canad. J. Math., vol. 33, pp. 437–449.
    • Canad. J. Math. , vol.33 , pp. 437-449
    • Bannai, E.1    Sloane, N.J.A.2
  • 2
    • 0002574523 scopus 로고
    • Some extreme forms defined in terms of Abelian groups
    • E. S. Barnes and G. E. Wall, “Some extreme forms defined in terms of Abelian groups,” J. Amer. Math. Soc., vol. 1, pp. 47–63, 1959.
    • (1959) J. Amer. Math. Soc. , vol.1 , pp. 47-63
    • Barnes, E.S.1    Wall, G.E.2
  • 3
    • 0003723775 scopus 로고
    • Zurich, Switzerland: B. I. Wissenschaftsverlag, Bibliographisches Institut
    • T. Beth, D. Jungnickel, and H. Lenz, Design Theory. Zurich, Switzerland: B. I. Wissenschaftsverlag, Bibliographisches Institut, 1985.
    • (1985) Design Theory
    • Beth, T.1    Jungnickel, D.2    Lenz, H.3
  • 4
    • 0015346083 scopus 로고
    • On the existence of group codes for the Gaussian channel
    • May
    • E. Biglieri and M. Elia, “On the existence of group codes for the Gaussian channel,” IEEE Trans. Inform. Theory, vol. IT-18, pp. 399–402, May 1972.
    • (1972) IEEE Trans. Inform. Theory , vol.IT-18 , pp. 399-402
    • Biglieri, E.1    Elia, M.2
  • 5
    • 0016999143 scopus 로고
    • Cyclic-group codes for the Gaussian channel
    • Sept.
    • E. Biglieri and M. Elia, “Cyclic-group codes for the Gaussian channel,” IEEE Trans. Inform. Theory, vol. IT-22, no. 5, pp. 624–629, Sept. 1976.
    • (1976) IEEE Trans. Inform. Theory , vol.IT-22 , Issue.5 , pp. 624-629
    • Biglieri, E.1    Elia, M.2
  • 6
    • 0017017530 scopus 로고
    • Optimum permutation modulation codes and their asymptotic performance
    • Nov.
    • —, “Optimum permutation modulation codes and their asymptotic performance,” IEEE Trans. Inform. Theory, vol. IT-22, no. 6, pp. 751–753, Nov. 1976.
    • (1976) IEEE Trans. Inform. Theory , vol.IT-22 , Issue.6 , pp. 751-753
    • Biglieri, E.1    Elia, M.2
  • 7
    • 0015431896 scopus 로고
    • Distance properties of group codes for the Gaussian channel
    • I. F. Blake, “Distance properties of group codes for the Gaussian channel,” SIAM J. Appl. Math., vol. 23, no. 3, 1972.
    • (1972) SIAM J. Appl. Math. , vol.23 , Issue.3
    • Blake, I.F.1
  • 8
    • 0015345949 scopus 로고
    • Codes over certain rings
    • May
    • —, “Codes over certain rings,” Inform. Contr., vol. 20, pp. 396–404, May 1972.
    • (1972) Inform. Contr. , vol.20 , pp. 396-404
    • Blake, I.F.1
  • 9
    • 0015956175 scopus 로고
    • Configuration matrices for group codes
    • Jan.
    • I. F. Blake, “Configuration matrices for group codes,” IEEE Trans. on Inform. Theory, vol. IT-20, pp. 95–100, Jan. 1974.
    • (1974) IEEE Trans. on Inform. Theory , vol.IT-20 , pp. 95-100
    • Blake, I.F.1
  • 10
    • 0015956996 scopus 로고
    • Permutation codes for discrete channels
    • Jan.
    • —, “Permutation codes for discrete channels,” IEEE Trans. Inform. Theory, vol. IT-20, pp. 138–140, Jan. 1974.
    • (1974) IEEE Trans. Inform. Theory , vol.IT-20 , pp. 138-140
    • Blake, I.F.1
  • 11
    • 0016619337 scopus 로고
    • Codes over integers residue rings
    • —, “Codes over integers residue rings,” Inform. Contr., vol. 29, pp. 295–300, 1975.
    • (1975) Inform. Contr. , vol.29 , pp. 295-300
    • Blake, I.F.1
  • 13
    • 0002897777 scopus 로고
    • Packing of spheres in spaces of constant curvature
    • K. Böröczky, “Packing of spheres in spaces of constant curvature,” Acta Math. Sci. Hungaricae, vol. 32, pp. 243–261, 1978.
    • (1978) Acta Math. Sci. Hungaricae , vol.32 , pp. 243-261
    • Böröczky, K.1
  • 17
    • 0001438198 scopus 로고
    • Strongly regular graphs having strongly regular subconstituents
    • P. J. Cameron, J.-M. Goethals, and J. J. Seidel, “Strongly regular graphs having strongly regular subconstituents,” J. Algebra, vol. 43, pp. 257–280, 1978.
    • (1978) J. Algebra , vol.43 , pp. 257-280
    • Cameron, P.J.1    Goethals, J.-M.2    Seidel, J.J.3
  • 18
    • 40949117697 scopus 로고
    • Resultat sur l'empilement de calottes egalessur une perisphere de Rn et correction a un travail anterieur
    • C. Chabauty, “Resultat sur l'empilement de calottes egalessur une perisphere de Rn et correction a un travail anterieur,” C.R.A.S, vol. 236, pp. 1462–1464, 1953.
    • (1953) C.R.A.S , vol.236 , pp. 1462-1464
    • Chabauty, C.1
  • 19
    • 0007841060 scopus 로고
    • The closest packing of equal circles on asphere
    • B. W. Clare and D. L. Kepert, “The closest packing of equal circles on asphere,” Proc. Roy. Soc. Land., vol. 405, pp. 329–344, 1986.
    • (1986) Proc. Roy. Soc. Land. , vol.405 , pp. 329-344
    • Clare, B.W.1    Kepert, D.L.2
  • 21
    • 0000243546 scopus 로고
    • Discrete groups generated by reflections
    • H. S. M. Coxeter, “Discrete groups generated by reflections,” Annal. Math., vol. 35, pp. 588–621, 1934.
    • (1934) Annal. Math. , vol.35 , pp. 588-621
    • Coxeter, H.S.M.1
  • 22
    • 0009936395 scopus 로고
    • An extreme duodenary form
    • H. S. M. Coxeter and J. A. Todd, “An extreme duodenary form,” Canad. J. Math., vol. 5, pp. 384–392, 1953.
    • (1953) Canad. J. Math. , vol.5 , pp. 384-392
    • Coxeter, H.S.M.1    Todd, J.A.2
  • 23
    • 0006131515 scopus 로고
    • The problem of packing a number of equal nonoverlapping circles on a sphere
    • H. S. M. Coxeter, “The problem of packing a number of equal nonoverlapping circles on a sphere,” Trans. N. Y. Acad. Sci. Ser. II, vol. 24, pp. 320–331, 1962.
    • (1962) Trans. N. Y. Acad. Sci. Ser. II , vol.24 , pp. 320-331
    • Coxeter, H.S.M.1
  • 24
    • 0013474953 scopus 로고
    • An upper bound for the number of equal nonoverlapping spheres that can touch another of the same size
    • Reprinted in H. S. M. Coxeter, Twelve Geometric Essays. Carbondale, IL: Southern Illinois Univ. Press
    • —, “An upper bound for the number of equal nonoverlapping spheres that can touch another of the same size,” in Proc. Symp. on Pure Mathematics, vol. VII, 1963, pp. 53–72. Reprinted in H. S. M. Coxeter, Twelve Geometric Essays. Carbondale, IL: Southern Illinois Univ. Press.
    • (1963) Proc. Symp. on Pure Mathematics , vol.7 , pp. 53-72
    • Coxeter, H.S.M.1
  • 28
    • 0015357424 scopus 로고
    • Bounds for unrestricted codes by linear programming
    • P. Delsarte, “Bounds for unrestricted codes by linear programming,” Philips Res. Rep., vol. 27, pp. 272–289, 1972.
    • (1972) Philips Res. Rep. , vol.27 , pp. 272-289
    • Delsarte, P.1
  • 29
    • 0016599548 scopus 로고
    • Bounds for systems of lines and jacobi polynomials
    • P. Delsarte, J. M. Goethals, and J. J. Seidel, “Bounds for systems of lines and jacobi polynomials,” Philips Res. Rep., vol. 30, pp. 91–105, 1975.
    • (1975) Philips Res. Rep. , vol.30 , pp. 91-105
    • Delsarte, P.1    Goethals, J.M.2    Seidel, J.J.3
  • 31
    • 84966254204 scopus 로고
    • An optimization problem for unitary and orthogonal representations of finite groups
    • D. Djokovic and I. F. Blake, “An optimization problem for unitary and orthogonal representations of finite groups,” Trans. Amer. Math. Soc., vol. 164, 1972.
    • (1972) Trans. Amer. Math. Soc. , vol.164
    • Djokovic, D.1    Blake, I.F.2
  • 32
    • 0026243454 scopus 로고
    • Concatenated method of construction of spherical codes in n-dimensional Euclidean space
    • S. M. Dodunekov, V. A. Zinoviev, and Th. Ericson, “Concatenated method of construction of spherical codes in n-dimensional Euclidean space,” Probl. Inform. Transm., vol. 27, no. 1, pp. 34–38, 1991.
    • (1991) Probl. Inform. Transm. , vol.27 , Issue.1 , pp. 34-38
    • Dodunekov, S.M.1    Zinoviev, V.A.2    Ericson, Th.3
  • 33
    • 0017512294 scopus 로고
    • On the existence of [M, n] group codes for the Gaussian channel with M and n odd
    • July
    • C. P. Downey and J. K. Karlof, “On the existence of [M, n] group codes for the Gaussian channel with M and n odd,” IEEE Trans. Inform. Theory, vol. IT-23, pp. 500–503, July 1977.
    • (1977) IEEE Trans. Inform. Theory , vol.IT-23 , pp. 500-503
    • Downey, C.P.1    Karlof, J.K.2
  • 34
    • 0018032061 scopus 로고
    • Optimal [M, 3] group codes for the Gaussian channel
    • Nov.
    • C. P. Downey and J. K. Karlof, “Optimal [M, 3] group codes for the Gaussian channel,” IEEE Trans. Inform. Theory, vol. IT-24, pp. 760–761, Nov. 1978.
    • (1978) IEEE Trans. Inform. Theory , vol.IT-24 , pp. 760-761
    • Downey, C.P.1    Karlof, J.K.2
  • 35
    • 0019496501 scopus 로고
    • Cascade decoding with respect to minimal generalized distance
    • I. I. Dumer, V. A. Zinoviev and V. V. Zyablov, “Cascade decoding with respect to minimal generalized distance,” Probl. Contr. Inform. Theory, vol. 10, no. 1, pp. 1–17, 1982.
    • (1982) Probl. Contr. Inform. Theory , vol.10 , Issue.1 , pp. 1-17
    • Dumer, I.I.1    Zinoviev, V.A.2    Zyablov, V.V.3
  • 36
    • 84938003473 scopus 로고
    • Performance of polyphase signals on a gaussian channel
    • G. Einarsson, “Performance of polyphase signals on a gaussian channel,” Ericsson Tech., no. 4, pp. 411–433, 1967.
    • (1967) Ericsson Tech. , Issue.4 , pp. 411-433
    • Einarsson, G.1
  • 37
    • 84939721150 scopus 로고
    • Polyphase coding for a Gaussian channel
    • —, “Polyphase coding for a Gaussian channel,” Ericsson Tech., no. 2, pp. 75–130, 1967.
    • (1967) Ericsson Tech. , Issue.2 , pp. 75-130
    • Einarsson, G.1
  • 38
    • 0005333604 scopus 로고
    • Bounds on the size of a code
    • M. Thoma and A. Wyner, Eds. New York: Springer-Verlag
    • Th. Ericson, “Bounds on the size of a code,” in Lecture Notes in Control and Inform. Sciences, vol. 128, M. Thoma and A. Wyner, Eds. New York: Springer-Verlag, 1989, pp. 45–72.
    • (1989) Lecture Notes in Control and Inform. Sciences , vol.128 , pp. 45-72
    • Ericson, Th.1
  • 44
    • 0026847778 scopus 로고
    • New packings on Euclidean sphere for finite dimensions
    • —, “New packings on Euclidean sphere for finite dimensions,” Probl. Inform. Transmission, vol. 28, no. 2, pp. 47–53, 1992.
    • (1992) Probl. Inform. Transmission , vol.28 , Issue.2 , pp. 47-53
    • Ericson, Th.1    Zinoviev, V.A.2
  • 45
    • 5844229360 scopus 로고
    • On spherical codes generating the kissing number in dimensions 8 and 24
    • —, “On spherical codes generating the kissing number in dimensions 8 and 24,” Discrete Math., vols. 106/107, pp. 199–207, 1992.
    • (1992) Discrete Math. , vol.106/107 , pp. 199-207
    • Ericson, Th.1    Zinoviev, V.A.2
  • 49
    • 33746350704 scopus 로고
    • Generalized minimum distance decoding
    • G. D. Forney, Jr., “Generalized minimum distance decoding,” IEEE Trans. Inform. Theory, IT-12, pp. 125–131, 1966.
    • (1966) IEEE Trans. Inform. Theory , vol.IT-12 , pp. 125-131
    • Forney, G.D.1
  • 50
  • 52
    • 0021306931 scopus 로고
    • Multidimensional signals for a continuous channel
    • V. V. Ginzburg, “Multidimensional signals for a continuous channel,” Probl. Inform. Transm., vol. 20, no. 1, pp. 28–46, 1984.
    • (1984) Probl. Inform. Transm. , vol.20 , Issue.1 , pp. 28-46
    • Ginzburg, V.V.1
  • 53
    • 0006886772 scopus 로고
    • On the regular and semi-regular figures in space of n dimensions
    • T. Gosset, “On the regular and semi-regular figures in space of n dimensions,” Messenger Math., vol. 29, pp. 43–48, 1900.
    • (1900) Messenger Math. , vol.29 , pp. 43-48
    • Gosset, T.1
  • 55
    • 0040773831 scopus 로고
    • Bemerkung der Reduction
    • (Grunert)
    • R. Hoppe, “Bemerkung der Reduction,” Archiv Math. Phys. (Grunert), vol. 56, pp. 307–312, 1874.
    • (1874) Archiv Math. Phys. , vol.56 , pp. 307-312
    • Hoppe, R.1
  • 56
    • 11144343315 scopus 로고
    • A new multilevel coding method using error-correcting codes
    • H. Imai and S. Hirakawa, “A new multilevel coding method using error-correcting codes,” IEEE Trans. Inform. Theory, vol. IT-23, pp. 371–377, 1977.
    • (1977) IEEE Trans. Inform. Theory , vol.IT-23 , pp. 371-377
    • Imai, H.1    Hirakawa, S.2
  • 57
    • 0015602477 scopus 로고
    • Commutative group codes for the Gaussian channel
    • Mar.
    • I. Ingemarsson, “Commutative group codes for the Gaussian channel,” IEEE Trans. Inform. Theory, vol. IT-19, pp. 215–219, Mar. 1973.
    • (1973) IEEE Trans. Inform. Theory , vol.IT-19 , pp. 215-219
    • Ingemarsson, I.1
  • 58
    • 33747359015 scopus 로고
    • Group codes for the Gaussian channel
    • M. Thoma and A. Wyner, Eds. New York: Springerhy-Verlag
    • —, “Group codes for the Gaussian channel,” in Lecture Notes in Control and Inform. Sciences, vol. 128, M. Thoma and A. Wyner, Eds. New York: Springerhy-Verlag, 1989, pp. 73–108.
    • (1989) Lecture Notes in Control and Inform. Sciences , vol.128 , pp. 73-108
    • Ingemarsson, I.1
  • 59
    • 0025484027 scopus 로고
    • Optimized permutation modulation
    • Sept.
    • —, “Optimized permutation modulation,” IEEE Trans. Inform. Theory, vol. 36, no. 5, pp. 1098–1100, Sept. 1990.
    • (1990) IEEE Trans. Inform. Theory , vol.36 , Issue.5 , pp. 1098-1100
    • Ingemarsson, I.1
  • 60
    • 0001336166 scopus 로고
    • A new upper bound for error-correcting codes
    • S. M. Johnson, “A new upper bound for error-correcting codes,” IEEE Trans. Inform. Theory, vol. IT-8, pp. 203–207, 1962.
    • (1962) IEEE Trans. Inform. Theory , vol.IT-8 , pp. 203-207
    • Johnson, S.M.1
  • 61
    • 0002468745 scopus 로고
    • Bounds for packings on a sphere and in space
    • G. A. Kabatiansky and V. I. Levenshtein, “Bounds for packings on a sphere and in space,” Probl. Inform. Transm., vol. 14, no. 1, pp. 1–17, 1978.
    • (1978) Probl. Inform. Transm. , vol.14 , Issue.1 , pp. 1-17
    • Kabatiansky, G.A.1    Levenshtein, V.I.2
  • 62
    • 0024702786 scopus 로고
    • Permutation codes for the Gaussian channel
    • July
    • J. K. Karlof, “Permutation codes for the Gaussian channel,” IEEE Trans. Inform. Theory, vol. 35, no. 4, pp. 726–732, July 1989.
    • (1989) IEEE Trans. Inform. Theory , vol.35 , Issue.4 , pp. 726-732
    • Karlof, J.K.1
  • 63
    • 84944027200 scopus 로고
    • Odd group codes for the Gaussian channel
    • J. K. Karlof and C. P. Downey, “Odd group codes for the Gaussian channel,” SIAM J. Appl. Math., vol. 34, pp. 715–716, 1978.
    • (1978) SIAM J. Appl. Math. , vol.34 , pp. 715-716
    • Karlof, J.K.1    Downey, C.P.2
  • 64
    • 0038257908 scopus 로고
    • A class of low-rate nonlinear codes
    • A. M. Kerdock, “A class of low-rate nonlinear codes,” Inform. Contr., vol. 20, pp. 182–187, 1972.
    • (1972) Inform. Contr. , vol.20 , pp. 182-187
    • Kerdock, A.M.1
  • 66
    • 0015027490 scopus 로고
    • How does a porcupine separate its quills?
    • Mar.
    • H. J. Landau, “How does a porcupine separate its quills?,” IEEE Trans. Inform. Theory, vol. IT-17, no. 2, pp. 157–161, Mar. 1971.
    • (1971) IEEE Trans. Inform. Theory , vol.IT-17 , Issue.2 , pp. 157-161
    • Landau, H.J.1
  • 67
    • 0001794073 scopus 로고
    • The problem of the thirteen spheres
    • J. Leech, “The problem of the thirteen spheres,” Math. Gaz., vol. 40, pp. 22–23, 1956.
    • (1956) Math. Gaz. , vol.40 , pp. 22-23
    • Leech, J.1
  • 68
    • 0039997205 scopus 로고
    • Some sphere packings in higher space
    • —, “Some sphere packings in higher space,” Canad. J. Math., vol. 16, pp. 657–682, 1964.
    • (1964) Canad. J. Math. , vol.16 , pp. 657-682
    • Leech, J.1
  • 69
    • 0001654568 scopus 로고
    • Notes on sphere packings
    • —, “Notes on sphere packings,” Canad. J. Math., vol. 19, pp. 251–267, 1967.
    • (1967) Canad. J. Math. , vol.19 , pp. 251-267
    • Leech, J.1
  • 70
    • 0001017029 scopus 로고
    • Sphere packings and error-correcting codes
    • J. Leech and N. J. A. Sloane, “Sphere packings and error-correcting codes,” Canad. J. Math., vol. 23, no. 4, pp. 718–745, 1971.
    • (1971) Canad. J. Math. , vol.23 , Issue.4 , pp. 718-745
    • Leech, J.1    Sloane, N.J.A.2
  • 71
    • 0001123945 scopus 로고
    • Equiangular lines
    • P. W. H. Lemmens and J. J. Seidel, “Equiangular lines,” J. Algebra, vol. 24, pp. 494–512, 1973.
    • (1973) J. Algebra , vol.24 , pp. 494-512
    • Lemmens, P.W.H.1    Seidel, J.J.2
  • 72
    • 0038247240 scopus 로고
    • On bounds for packings in n-dimensional Euclidean space
    • V. I. Levenshtein, “On bounds for packings in n-dimensional Euclidean space,” Sov. Math.- Dokl., vol. 20, no. 2, pp. 417–421, 1979.
    • (1979) Sov. Math.- Dokl. , vol.20 , Issue.2 , pp. 417-421
    • Levenshtein, V.I.1
  • 73
    • 0002613871 scopus 로고
    • Bounds for packings of metric spaces and some of their applications
    • Moscow, USSR: Nauka, (in Russian)
    • —, “Bounds for packings of metric spaces and some of their applications,” Problemy Kibernetiki, vol. 40. Moscow, USSR: Nauka, 1983, pp. 43–110 (in Russian).
    • (1983) Problemy Kibernetiki , vol.40 , pp. 43-110
    • Levenshtein, V.I.1
  • 74
    • 34249842879 scopus 로고
    • Designs as maximum codes in polynomial metric spaces
    • —, “Designs as maximum codes in polynomial metric spaces,” Acta Appl. Mathematicae, vol. 29, no. 99, pp. 11–82, 1992.
    • (1992) Acta Appl. Mathematicae , vol.29 , Issue.99 , pp. 11-82
    • Levenshtein, V.I.1
  • 75
    • 84937994403 scopus 로고
    • Hamming associattion schemes and codes on spheres
    • May
    • S. P. Lloyd, “Hamming associattion schemes and codes on spheres,” SIAM J. Math. Anal., vol. 11, no. 3, pp. 488–505, May 1980.
    • (1980) SIAM J. Math. Anal. , vol.11 , Issue.3 , pp. 488-505
    • Lloyd, S.P.1
  • 76
    • 0010080385 scopus 로고
    • The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere
    • A. L. MacKay, “The packing of three-dimensional spheres on the surface of a four-dimensional hypersphere,” J. Phys., vol. A13, pp. 3373–3379, 1980.
    • (1980) J. Phys. , vol.A13 , pp. 3373-3379
    • MacKay, A.L.1
  • 78
    • 4243772328 scopus 로고
    • Linear block codes over rings for phase shift keying
    • (Dissertations), Linköping, Sweden
    • M. Nilsson, “Linear block codes over rings for phase shift keying,” in Linköping Studies in Science and Technology (Dissertations), no. 321, Linköping, Sweden, 1993.
    • (1993) Linköping Studies in Science and Technology , Issue.321
    • Nilsson, M.1
  • 79
    • 0001179224 scopus 로고
    • New upper bounds on the number of unit spheres that can touch a unit sphere in n dimensions
    • A. M. Odlyzko and N. J. A. Sloane, “New upper bounds on the number of unit spheres that can touch a unit sphere in n dimensions,” J. Combin. Theory, vol. A 26, pp. 210–214, 1979.
    • (1979) J. Combin. Theory , vol.A 26 , pp. 210-214
    • Odlyzko, A.M.1    Sloane, N.J.A.2
  • 80
    • 84938004954 scopus 로고
    • Performance of phase- and amplitude-modulated signals on a Gaussian channel
    • R. Ottosson, “Performance of phase- and amplitude-modulated signals on a Gaussian channel,” Ericsson Tech., no. 3, pp. 153–198, 1969.
    • (1969) Ericsson Tech. , Issue.3 , pp. 153-198
    • Ottosson, R.1
  • 81
    • 0015068255 scopus 로고
    • Group codes for phase- and amplitude-modulated signals on a Gaussian channel
    • May
    • —, “Group codes for phase- and amplitude-modulated signals on a Gaussian channel,” IEEE Trans. Inform. Theory, vol. IT-17, pp. 315–321, May 1971.
    • (1971) IEEE Trans. Inform. Theory , vol.IT-17 , pp. 315-321
    • Ottosson, R.1
  • 82
    • 0022812172 scopus 로고
    • Bounds for codes over the unit circle
    • P. Piret, “Bounds for codes over the unit circle,” IEEE Trans. Inform. Theory, vol. IT-32, no. 6, pp. 760–767, 1986.
    • (1986) IEEE Trans. Inform. Theory , vol.IT-32 , Issue.6 , pp. 760-767
    • Piret, P.1
  • 83
    • 84937994671 scopus 로고
    • Characterisations of modulation and encoding systems as concatenated codes
    • S. L. Portnoi, “Characterisations of modulation and encoding systems as concatenated codes,” Probl. Inform. Transm., vol. 21, no. 3, pp. 14–27, 1985.
    • (1985) Probl. Inform. Transm. , vol.21 , Issue.3 , pp. 14-27
    • Portnoi, S.L.1
  • 84
    • 84973938095 scopus 로고
    • The closest packing of spherical caps in n dimensions
    • R. A. Rankin, “The closest packing of spherical caps in n dimensions,” Proc. Glascow Math. Assoc., vol. 2, pp. 139–144, 1955.
    • (1955) Proc. Glascow Math. Assoc. , vol.2 , pp. 139-144
    • Rankin, R.A.1
  • 85
    • 0013008043 scopus 로고
    • Arrangements of 24 points on a sphere
    • R. M. Robinson, “Arrangements of 24 points on a sphere,” Math. Ann., vol. 144, pp. 17–48, 1961.
    • (1961) Math. Ann. , vol.144 , pp. 17-48
    • Robinson, R.M.1
  • 86
    • 0022795919 scopus 로고
    • A class of optimum block codes in signal space
    • S. I. Sayegh, “A class of optimum block codes in signal space,” IEEE Trans. Commun., vol. COM-34, no. 10, pp. 1043–1045, 1986.
    • (1986) IEEE Trans. Commun. , vol.COM-34 , Issue.10 , pp. 1043-1045
    • Sayegh, S.I.1
  • 87
    • 33746051615 scopus 로고
    • Auf welcher Kugel haben 5, 6, 7, oder 8 Punkte mit Mindestabstand Eins Platz?
    • K. Schütte and B. L. van der Waerden, “Auf welcher Kugel haben 5, 6, 7, oder 8 Punkte mit Mindestabstand Eins Platz?,” Math. Ann., vol. 123, pp. 96–124, 1951.
    • (1951) Math. Ann. , vol.123 , pp. 96-124
    • Schütte, K.1    van der Waerden, B.L.2
  • 88
    • 84907062399 scopus 로고
    • Probability of error for optimal codes in a Gaussian channel
    • C. E. Shannon, “Probability of error for optimal codes in a Gaussian channel,” Bell Syst. Tech. J., vol. 38, pp. 611–656, 1959.
    • (1959) Bell Syst. Tech. J. , vol.38 , pp. 611-656
    • Shannon, C.E.1
  • 89
    • 0010178598 scopus 로고
    • On the densest packing of balls on the surface of an n-dimensional Euclidean sphere and the number of binary code vectors with a given code distance
    • V. M. Sidelnikov, “On the densest packing of balls on the surface of an n-dimensional Euclidean sphere and the number of binary code vectors with a given code distance,” Soviet Math.-Dokl., vol. 14, pp. 1851–1855, 1973.
    • (1973) Soviet Math.-Dokl. , vol.14 , pp. 1851-1855
    • Sidelnikov, V.M.1
  • 90
    • 84892180578 scopus 로고
    • Permutatiom modulation
    • Mar.
    • D. Slepian, “Permutatiom modulation,” Proc. IEEE, vol. 53, no. 3, pp. 228–236, Mar. 1965.
    • (1965) Proc. IEEE , vol.53 , Issue.3 , pp. 228-236
    • Slepian, D.1
  • 91
    • 80054814722 scopus 로고
    • Group codes for the Gaussian channel
    • Apr.
    • —, “Group codes for the Gaussian channel,” Bell Syst. Tech. J., vol. 47, no. 4, pp. 575–602, Apr. 1968.
    • (1968) Bell Syst. Tech. J. , vol.47 , Issue.4 , pp. 575-602
    • Slepian, D.1
  • 92
    • 0019566103 scopus 로고
    • Tables of sphere packings and spherical codes
    • N. J. A. Sloane, “Tables of sphere packings and spherical codes,” IEEE Trans. Inform. Theory, vol. IT-27, pp. 327–338, 1981.
    • (1981) IEEE Trans. Inform. Theory , vol.IT-27 , pp. 327-338
    • Sloane, N.J.A.1
  • 93
    • 33747496070 scopus 로고
    • Recent bounds for codes, sphere packing and related problems obtained by linear programming and other methods
    • —, “Recent bounds for codes, sphere packing and related problems obtained by linear programming and other methods,” Contemp. Math., vol. 9, pp. 153–185, 1982.
    • (1982) Contemp. Math. , vol.9 , pp. 153-185
    • Sloane, N.J.A.1
  • 94
    • 0019343223 scopus 로고
    • Channel coding with multilevel/phase signals
    • Jan.
    • G. Ungerboeck, “Channel coding with multilevel/phase signals,” IEEE Trans. Inform. Theory, vol. IT-28, no. 1, pp. 55–67, Jan. 1982.
    • (1982) IEEE Trans. Inform. Theory , vol.IT-28 , Issue.1 , pp. 55-67
    • Ungerboeck, G.1
  • 95
    • 0000128818 scopus 로고
    • Capabilities of bounded discrepancy decoding
    • A. D. Wyner, “Capabilities of bounded discrepancy decoding,” Bell Syst. Tech. J., vol. 44, pp. 1061–1122, 1965.
    • (1965) Bell Syst. Tech. J. , vol.44 , pp. 1061-1122
    • Wyner, A.D.1
  • 96
    • 33749981019 scopus 로고
    • A class of codes for polyphase signals on a bandlimited Gaussian channel
    • July
    • L. H. Zetterberg, “A class of codes for polyphase signals on a bandlimited Gaussian channel,” IEEE Trans. Inform. Theory, vol. IT-11, pp. 385–395, July 1965.
    • (1965) IEEE Trans. Inform. Theory , vol.IT-11 , pp. 385-395
    • Zetterberg, L.H.1
  • 97
    • 84930556210 scopus 로고
    • Detection of a class of coded and phase-modulated signals
    • Apr.
    • —, “Detection of a class of coded and phase-modulated signals,” IEEE Trans. Inform. Theory, vol. IT-12, pp. 153–161, Apr. 1966.
    • (1966) IEEE Trans. Inform. Theory , vol.IT-12 , pp. 153-161
    • Zetterberg, L.H.1
  • 98
    • 0017533091 scopus 로고
    • Codes for the combined phase and amplitude modulated signals in a four-dimensional space
    • Sept.
    • L. H. Zetterberg and H. Brändsträm, “Codes for the combined phase and amplitude modulated signals in a four-dimensional space,” IEEE Trans. Commun., vol. COM-25, pp. 943–950, Sept. 1977.
    • (1977) IEEE Trans. Commun. , vol.COM-25 , pp. 943-950
    • Zetterberg, L.H.1    Brändsträm, H.2
  • 99
    • 0042385445 scopus 로고
    • Generalized concatenated codes
    • V. A. Zinoviev, “Generalized concatenated codes,” Probl. Inform. Transm., vol. 12, no. 1, pp. 5–15, 1976.
    • (1976) Probl. Inform. Transm. , vol.12 , Issue.1 , pp. 5-15
    • Zinoviev, V.A.1
  • 100
    • 84937998290 scopus 로고
    • Decoding of nonlinear generalized concatenated codes
    • V. A. Zinoviev and V. V. Zyablov, “Decoding of nonlinear generalized concatenated codes,” Probl. Inform. Transm., vol. 14, no. 2, pp. 46–52, 1978.
    • (1978) Probl. Inform. Transm. , vol.14 , Issue.2 , pp. 46-52
    • Zinoviev, V.A.1    Zyablov, V.V.2
  • 102
    • 0023379780 scopus 로고
    • On one modulation coding system for a Gaussian channel
    • V. V. Zyablov and S. L. Portnoi, “On one modulation coding system for a Gaussian channel,” Probl. Inform. Transm., vol. 23, no. 3, pp. 18–26, 1987.
    • (1987) Probl. Inform. Transm. , vol.23 , Issue.3 , pp. 18-26
    • Zyablov, V.V.1    Portnoi, S.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.