메뉴 건너뛰기




Volumn 102, Issue 1-2, 2000, Pages 115-131

An introduction to cocyclic generalised Hadamard matrices

Author keywords

Generalised Hadamard matrix; Orthogonal cocycle; Semiregular relative difference set

Indexed keywords


EID: 0005777050     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(99)00233-4     Document Type: Article
Times cited : (10)

References (50)
  • 1
    • 0005075342 scopus 로고    scopus 로고
    • New self-dual codes from cocyclic Hadamard matrices
    • Baliga A. New self-dual codes from cocyclic Hadamard matrices. J. Combin. Math. Combin. Comput. 28:1998;7-14.
    • (1998) J. Combin. Math. Combin. Comput. , vol.28 , pp. 7-14
    • Baliga, A.1
  • 4
    • 0347434544 scopus 로고
    • On the construction of n-dimensional designs from 2-dimensional designs
    • de Launey W. On the construction of. n -dimensional designs from 2-dimensional designs Australas. J. Combin. 1:1990;67-81.
    • (1990) Australas. J. Combin. , vol.1 , pp. 67-81
    • De Launey, W.1
  • 5
    • 0001910745 scopus 로고
    • Generalised Hadamard matrices which are developed modulo a group
    • de Launey W. Generalised Hadamard matrices which are developed modulo a group. Discrete Math. 104:1992;49-65.
    • (1992) Discrete Math. , vol.104 , pp. 49-65
    • De Launey, W.1
  • 7
    • 0001949013 scopus 로고
    • A weak difference set construction for higher dimensional designs
    • de Launey W., Horadam K.J. A weak difference set construction for higher dimensional designs. Des. Codes Cryptography. 3:1993;75-87.
    • (1993) Des. Codes Cryptography , vol.3 , pp. 75-87
    • De Launey, W.1    Horadam, K.J.2
  • 9
    • 0346836861 scopus 로고    scopus 로고
    • On cocyclic weighing matrices and the regular group of actions of certain Paley matrices
    • de Launey W., Stafford R. On cocyclic weighing matrices and the regular group of actions of certain Paley matrices. Discrete Appl. Math. 102:2000;63-101.
    • (2000) Discrete Appl. Math. , vol.102 , pp. 63-101
    • De Launey, W.1    Stafford, R.2
  • 10
    • 0348064851 scopus 로고
    • Transgression and the calculation of cocyclic matrices
    • Flannery D.L. Transgression and the calculation of cocyclic matrices. Australas. J. Combin. 11:1995;67-78.
    • (1995) Australas. J. Combin. , vol.11 , pp. 67-78
    • Flannery, D.L.1
  • 11
    • 0030604984 scopus 로고    scopus 로고
    • Calculation of cocyclic matrices
    • Flannery D.L. Calculation of cocyclic matrices. J. Pure Appl. Algebra. 112:1996;181-190.
    • (1996) J. Pure Appl. Algebra , vol.112 , pp. 181-190
    • Flannery, D.L.1
  • 12
    • 0031570642 scopus 로고    scopus 로고
    • Cocyclic Hadamard matrices and Hadamard groups are equivalent
    • Flannery D.L. Cocyclic Hadamard matrices and Hadamard groups are equivalent. J. Algebra. 192:1997;749-779.
    • (1997) J. Algebra , vol.192 , pp. 749-779
    • Flannery, D.L.1
  • 13
    • 0347434506 scopus 로고    scopus 로고
    • Computing 2-cocycles for central extensions and relative difference sets
    • to appear
    • D.L. Flannery, E.A. O'Brien, Computing 2-cocycles for central extensions and relative difference sets, Comm. Algebra (1999) , to appear.
    • (1999) Comm. Algebra
    • Flannery, D.L.1    O'Brien, E.A.2
  • 14
    • 0010995598 scopus 로고    scopus 로고
    • Progress in cocyclic matrices
    • Horadam K.J. Progress in cocyclic matrices. Congr. Numer. 118:1996;161-171.
    • (1996) Congr. Numer. , vol.118 , pp. 161-171
    • Horadam, K.J.1
  • 16
    • 22844454113 scopus 로고    scopus 로고
    • Sequences from cocycles
    • in: eds. M. Fossorier et al., Springer, Berlin
    • K.J. Horadam, Sequences from cocycles, in: AAECC-13, Lecture Notes in Computer Science, Vol. 1719, eds. M. Fossorier et al., Springer, Berlin, 1999, pp. 121-130.
    • (1999) AAECC-13, Lecture Notes in Computer Science , vol.1719 , pp. 121-130
    • Horadam, K.J.1
  • 17
    • 0348064813 scopus 로고    scopus 로고
    • a,1)-difference sets
    • Mathematics Department, RMIT, May
    • a,1) -difference sets, Research Report No. 7, Mathematics Department, RMIT, May 1998.
    • (1998) Research Report , vol.7
    • Horadam, K.J.1
  • 18
    • 0347434505 scopus 로고    scopus 로고
    • Equivalence classes of central semiregular relative difference sets
    • to appear
    • K.J. Horadam, Equivalence classes of central semiregular relative difference sets, J. Combin. Designs (2000), to appear.
    • (2000) J. Combin. Designs
    • Horadam, K.J.1
  • 19
    • 0001737513 scopus 로고
    • Cocyclic development of designs
    • Erratum 3 (1994) 129
    • K.J. Horadam, W. de Launey, Cocyclic development of designs, J. Algebraic Combin. 2 (1993) 267-290, Erratum 3 (1994) 129.
    • (1993) J. Algebraic Combin. , vol.2 , pp. 267-290
    • Horadam, K.J.1    De Launey, W.2
  • 20
    • 0040411238 scopus 로고
    • Generation of cocyclic Hadamard matrices
    • in: W. Bosma, A. van der Poorten (Eds.), Kluwer Academic, Dordrecht, (Chapter 20)
    • K.J. Horadam, W. de Launey, Generation of cocyclic Hadamard matrices, in: W. Bosma, A. van der Poorten (Eds.), Computational Algebra and Number Theory, Kluwer Academic, Dordrecht, 1995, pp. 279-290 (Chapter 20).
    • (1995) Computational Algebra and Number Theory , pp. 279-290
    • Horadam, K.J.1    De Launey, W.2
  • 21
    • 0346173388 scopus 로고    scopus 로고
    • Construction of proper higher dimensional Hadamard matrices from perfect binary arrays
    • Horadam K.J., Lin C. Construction of proper higher dimensional Hadamard matrices from perfect binary arrays. J. Combin. Math. Combin. Comput. 28:1998;237-248.
    • (1998) J. Combin. Math. Combin. Comput. , vol.28 , pp. 237-248
    • Horadam, K.J.1    Lin, C.2
  • 22
    • 0005849497 scopus 로고    scopus 로고
    • Codes from cocycles
    • in: T. Mora, H. Mattson (Eds.), Springer, Berlin
    • K.J. Horadam, A.A.I. Perera, Codes from cocycles, in: T. Mora, H. Mattson (Eds.), AAECC-12, Lecture Notes in Computer Science, vol. 1255, Springer, Berlin, 1997, pp. 151-163.
    • (1997) AAECC-12, Lecture Notes in Computer Science , vol.1255 , pp. 151-163
    • Horadam, K.J.1    Perera, A.A.I.2
  • 23
  • 24
    • 33745657308 scopus 로고    scopus 로고
    • Characteristic functions of relative difference sets, correlated sequences and Hadamard matrices
    • in: eds. M. Fossorier et al., Springer, Berlin
    • G. Hughes, Characteristic functions of relative difference sets, correlated sequences and Hadamard matrices, in: AAECC-13, Lecture Notes in Computer Science, Vol. 1719, eds. M. Fossorier et al., Springer, Berlin, 1999, pp. 346-354.
    • (1999) AAECC-13, Lecture Notes in Computer Science , vol.1719 , pp. 346-354
    • Hughes, G.1
  • 25
    • 0034396222 scopus 로고    scopus 로고
    • Non-splitting abelian (4t, 2, 4t, 2t)-relative difference sets and Hadamard cocycles
    • to appear
    • G. Hughes, Non-splitting abelian (4t, 2, 4t, 2t) -relative difference sets and Hadamard cocycles, Eur. J. Combin. (2000), to appear.
    • (2000) Eur. J. Combin.
    • Hughes, G.1
  • 26
    • 0347434539 scopus 로고
    • Note on Hadamard matrices of type Q
    • Ito N. Note on Hadamard matrices of type Q. Studia Sci. Math. Hungar. 16:1981;389-393.
    • (1981) Studia Sci. Math. Hungar. , vol.16 , pp. 389-393
    • Ito, N.1
  • 27
    • 0000778285 scopus 로고
    • On Hadamard groups
    • Ito N. On Hadamard groups. J. Algebra. 168:1994;981-987.
    • (1994) J. Algebra , vol.168 , pp. 981-987
    • Ito, N.1
  • 28
    • 0000778286 scopus 로고
    • On Hadamard groups II
    • Ito N. On Hadamard groups II. J. Algebra. 169:1994;936-942.
    • (1994) J. Algebra , vol.169 , pp. 936-942
    • Ito, N.1
  • 29
    • 0040106008 scopus 로고    scopus 로고
    • Remarks on Hadamard groups
    • Ito N. Remarks on Hadamard groups. Kyushu J. Math. 50:1996;1-9.
    • (1996) Kyushu J. Math. , vol.50 , pp. 1-9
    • Ito, N.1
  • 30
    • 0038477493 scopus 로고    scopus 로고
    • Cocyclic generalised Hadamard matrices and central relative difference sets
    • Perera A.A.I., Horadam K.J. Cocyclic generalised Hadamard matrices and central relative difference sets. Des. Codes Cryptography. 15:1998;187-200.
    • (1998) Des. Codes Cryptography , vol.15 , pp. 187-200
    • Perera, A.A.I.1    Horadam, K.J.2
  • 31
    • 0348064812 scopus 로고    scopus 로고
    • Ph. D. Thesis, RMIT University, Melbourne, Australia, submitted June
    • A.A.I. Perera, Orthogonal cocycles, Ph. D. Thesis, RMIT University, Melbourne, Australia, submitted June 1999.
    • (1999) Orthogonal Cocycles
    • Perera, A.A.I.1
  • 35
    • 84966254660 scopus 로고
    • Generalised Hadamard matrices
    • Butson A.T. Generalised Hadamard matrices. Proc. Amer. Math. Soc. 13:1962;894-898.
    • (1962) Proc. Amer. Math. Soc. , vol.13 , pp. 894-898
    • Butson, A.T.1
  • 37
    • 0031256841 scopus 로고    scopus 로고
    • A unifying construction for difference sets
    • Davis J.A., Jedwab J. A unifying construction for difference sets. J. Combin. Theory Ser. A. 80:1997;13-78.
    • (1997) J. Combin. Theory Ser. a , vol.80 , pp. 13-78
    • Davis, J.A.1    Jedwab, J.2
  • 38
    • 0001882036 scopus 로고
    • A survey of generalised Hadamard matrices and difference matrices D(k, λ ; G) with large k
    • de Launey W. A survey of generalised Hadamard matrices and difference matrices. D(k, λ ; G) with large k Utilitas Math. 30:1986;5-29.
    • (1986) Utilitas Math. , vol.30 , pp. 5-29
    • De Launey, W.1
  • 39
    • 0043107144 scopus 로고
    • Square GBRDs over non-abelian groups
    • de Launey W. Square GBRDs over non-abelian groups. Ars Combin. 27:1989;40-49.
    • (1989) Ars Combin. , vol.27 , pp. 40-49
    • De Launey, W.1
  • 40
    • 0026155690 scopus 로고
    • t and Reed-Muller codes
    • t and Reed-Muller codes IEEE Trans-IT. 37:1991;664-667.
    • (1991) IEEE Trans-IT , vol.37 , pp. 664-667
    • De Launey, W.1
  • 41
    • 0000648914 scopus 로고
    • Partial λ-geometries and generalised Hadamard matrices
    • Drake D.A. Partial. λ -geometries and generalised Hadamard matrices Canadian J. Math. 31:1979;617-627.
    • (1979) Canadian J. Math. , vol.31 , pp. 617-627
    • Drake, D.A.1
  • 43
    • 0002283175 scopus 로고
    • Generalised perfect binary arrays and Menon difference sets
    • Jedwab J. Generalised perfect binary arrays and Menon difference sets. Des. Codes Cryptography. 2:1992;19-68.
    • (1992) Des. Codes Cryptography , vol.2 , pp. 19-68
    • Jedwab, J.1
  • 44
    • 0000279759 scopus 로고
    • On automorphism groups of divisible designs
    • Jungnickel D. On automorphism groups of divisible designs. Canadian J. Math. 24:1982;257-297.
    • (1982) Canadian J. Math. , vol.24 , pp. 257-297
    • Jungnickel, D.1
  • 46
    • 0002896677 scopus 로고
    • Maximal q-ary codes and Plotkin's bound
    • Mackenzie C., Seberry J. Maximal. q -ary codes and Plotkin's bound Ars Combin. 26B:1988;37-50.
    • (1988) Ars Combin. , vol.26 , pp. 37-50
    • MacKenzie, C.1    Seberry, J.2
  • 49
    • 0001986729 scopus 로고    scopus 로고
    • A survey on relative difference sets
    • in Walter de Gruyter, New York
    • A. Pott, A survey on relative difference sets, in Groups, Difference Sets and the Monster, Walter de Gruyter, New York, 1996.
    • (1996) Groups, Difference Sets and the Monster
    • Pott, A.1
  • 50
    • 0000361595 scopus 로고
    • Self-orthogonal designs and extremal doubly even codes
    • Tonchev V.D. Self-orthogonal designs and extremal doubly even codes. J. Combin. Theory Ser. A. 52:1989;197-205.
    • (1989) J. Combin. Theory Ser. a , vol.52 , pp. 197-205
    • Tonchev, V.D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.