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Volumn 38, Issue 6, 1992, Pages 1663-1676

Decoding Geometric Goppa Codes Using an Extra Place

Author keywords

affine ring; algebraic geometric codes; decoding; Geometric Goppa codes; isometry; key equation

Indexed keywords

ALGORITHMS;

EID: 0026953491     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.165441     Document Type: Article
Times cited : (41)

References (30)
  • 1
    • 0004019233 scopus 로고
    • Introduction to the theory of algebraic functions in one variable
    • C. Chevalley, “Introduction to the theory of algebraic functions in one variable,” Mathematical Surveys VI. Providence: AMS, 1951.
    • (1951) Mathematical Surveys VI. Providence: AMS
    • Chevalley, C.1
  • 2
    • 17044410466 scopus 로고
    • The symmetry of the Weierstrass generalized semigroups and affine embedding
    • F. Delgado, “The symmetry of the Weierstrass generalized semigroups and affine embedding,” Proc. Amer. Math. Soc., vol. 108, pp. 627-631, 1990.
    • (1990) Proc. Amer. Math. Soc. , vol.108 , pp. 627-631
    • Delgado, F.1
  • 3
    • 38249037233 scopus 로고
    • Elliptic codes over fields of characteristic 2
    • Y. Driencourt and J. F. Michon, “Elliptic codes over fields of characteristic 2,” J. Pure Appl. Algebra, vol. 45, 15-39, 1987.
    • (1987) J. Pure Appl. Algebra , vol.45 , pp. 15-39
    • Driencourt, Y.1    Michon, J.F.2
  • 7
    • 0002417983 scopus 로고
    • Codes associated with divisors
    • Translation: Probl. Inform. Transm., vol.13, pp.22-26, 1977
    • V. D. Goppa, “Codes associated with divisors,” Probl. Peredachi Inform, vol. 13, no. 1, pp. 33-39, 1977. Translation: Probl. Inform. Transm., vol.13, pp.22-26, 1977
    • (1977) Probl. Peredachi Inform , vol.13 , Issue.1 , pp. 33-39
    • Goppa, V.D.1
  • 8
    • 0000588580 scopus 로고
    • Codes on algebraic curves
    • Translation: Soviet Math. Dokl. vol.24, pp. 170-172 1981
    • “Codes on algebraic curves,” Dokl. Akad. Nauk SSSR, vol. 259, pp. 1289-1290, 1981. Translation: Soviet Math. Dokl. vol.24, pp. 170-172, 1981
    • (1981) Dokl. Akad. Nauk SSSR , vol.259 , pp. 1289-1290
  • 9
    • 0002058835 scopus 로고
    • Algebraic-geometric codes
    • Translation: Math. USSR Izvestija, vol. 21, pp. 75-91 1983
    • “Algebraic-geometric codes,” Izv. Akad. Nauk SSSR, vol. 46, 1982. Translation: Math. USSR Izvestija, vol. 21, pp. 75-91, 1983
    • (1982) Izv. Akad. Nauk SSSR , vol.46
  • 10
    • 84955593036 scopus 로고
    • Codes and information
    • “Codes and information,” Russian Math. Surveys, vol. 39, pp. 87-141, 1984.
    • (1984) Russian Math. Surveys , vol.39 , pp. 87-141
  • 11
    • 84927056568 scopus 로고
    • Ph.D. thesis, Technical Univ. of Denmark, May
    • C. D. Jensen, “Codes and geometry,” Ph.D. thesis, Technical Univ. of Denmark, May 1991.
    • (1991) Codes and geometry
    • Jensen, C.D.1
  • 16
    • 0024766653 scopus 로고
    • On a decoding algorithm for codes on maximal curves
    • Nov.
    • R. Pellikaan, “On a decoding algorithm for codes on maximal curves,” IEEE Trans. Inform. Theory, vol. 35, pp. 1228-1232, Nov. 1989.
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 1228-1232
    • Pellikaan, R.1
  • 17
    • 0026151644 scopus 로고
    • Which linear codes are algebraic-geometric?
    • pt. 1, May
    • R. Pellikaan, B.-Z. Shen, and G. J. M. Wee, “Which linear codes are algebraic-geometric?” IEEE Trans. Inform. Theory, vol. 37, pt. 1, pp. 583-602, May 1991.
    • (1991) IEEE Trans. Inform. Theory , vol.37 , pp. 583-602
    • Pellikaan, R.1    Shen, B.-Z.2    Wee, G.J.M.3
  • 19
    • 0001631732 scopus 로고
    • Weierstrass points and monomial curves
    • D. S. Rim and M. A. Vitulli, “Weierstrass points and monomial curves,” J. Algebra, vol. 48, pp. 454-476, 1977.
    • (1977) J. Algebra , vol.48 , pp. 454-476
    • Rim, D.S.1    Vitulli, M.A.2
  • 20
    • 0010081823 scopus 로고
    • On planar curves
    • A. Sathaye, “On planar curves,” Amer. J. Math., vol. 99, pp. 1105-1135, 1974.
    • (1974) Amer. J. Math. , vol.99 , pp. 1105-1135
    • Sathaye, A.1
  • 21
    • 84941538197 scopus 로고    scopus 로고
    • Solving a congruence on a graded algebra by a subresultant sequence and its application
    • to appear in
    • B.-Z. Shen, “Solving a congruence on a graded algebra by a subresultant sequence and its application,” to appear in J. Symbolic Computat.
    • J. Symbolic Computat.
    • Shen, B.-Z.1
  • 23
    • 0025484013 scopus 로고
    • On the decoding of algebraic-geometric codes
    • Sept.
    • A. Skorobogatov and S. VladuJ, “On the decoding of algebraic-geometric codes,” IEEE Trans. Inform. Theory, vol. 36, pp. 10511060, Sept. 1990.
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 1051-1060
    • Skorobogatov, A.1    VladuJ, S.2
  • 24
    • 0001243944 scopus 로고
    • Uber die Automorphismengruppe eines algebraischen Funktionenkorpers von Primzablcharakteristik, teil 2
    • H. Stichtenoth, “Uber die Automorphismengruppe eines algebraischen Funktionenkorpers von Primzablcharakteristik, teil 2, Arch. Math., vol. 24, pp. 615-631, 1973.
    • (1973) Arch. Math. , vol.24 , pp. 615-631
    • Stichtenoth, H.1
  • 25
    • 0024079322 scopus 로고
    • A note on Hermitian codes over GF(q2)
    • pt. 2, Sept.
    • “A note on Hermitian codes over GF(q2),” IEEE Trans. Inform. Theory, vol. 34, pt. 2, pp. 1345-1348, Sept. 1988.
    • (1988) IEEE Trans. Inform. Theory , vol.34 , pp. 1345-1348
  • 26
    • 38249018842 scopus 로고
    • On the automorphisms of geometric Goppa codes
    • “On the automorphisms of geometric Goppa codes,” J. Algebra, vol. 130, pp. 113-121, 1990.
    • (1990) J. Algebra , vol.130 , pp. 113-121
  • 27
    • 84939392411 scopus 로고
    • Remarks on codes from Hermitian curves
    • July
    • H. J. Tiersma, “Remarks on codes from Hermitian curves,” IEEE Trans. Inform. Theory, vol. 33, pp. 605-609, July 1987.
    • (1987) IEEE Trans. Inform. Theory , vol.33 , pp. 605-609
    • Tiersma, H.J.1
  • 28
    • 84859625236 scopus 로고
    • Modular curves, Shimura curves and Goppa codes, better than Varshamov-Gilbert bound
    • M. A. Tsfasman, S. G. Vladut, and T. Zink, “Modular curves, Shimura curves and Goppa codes, better than Varshamov-Gilbert bound,” Math. Nachrichten, vol. 109, pp. 21-28, 1982.
    • (1982) Math. Nachrichten , vol.109 , pp. 21-28
    • Tsfasman, M.A.1    Vladut, S.G.2    Zink, T.3
  • 30
    • 0025521995 scopus 로고
    • On the decoding of algebraic-geometric codes over Fq for q > 16
    • Nov.
    • S. G. Vladut, “On the decoding of algebraic-geometric codes over Fq for q > 16”, IEEE Trans. Inform. Theory, vol. 36, pp. 1461-1463, Nov. 1990.
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 1461-1463
    • Vladut, S.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.