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F_4上的3维最优自正交码 被引量：3

Optimal quaternary self-orthogonal codes of dimension three
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摘要 目的研究F4上维数为3的最优(或拟最优)自正交码的码长与极小距离之间的关系。方法组合方法。结果构造出码长n≥21的3维最优(或拟最优)自正交码的生成矩阵,确定出了其中达到Griesmer界的码。结论给出了3维的最优自正交码码长与距离的规律。 Aim The relations between length and minimum distance of 3 dimension optimal or near optimal quaternary self-orthogonal codes are investigated. Methods Combinatorial method is used to construct 3 dimension optimal or near optimal quaternary self-orthogonal codes for length. Results The generator matrices of such optimal or near optimal self-orthogonal codes are constructed, and the optimal self-orthogonal codes that achieve the Griesmer bound are determined. Conclusion The characterization of optimal self-orthogonal codes of dimension 3 is given.
作者 李益群 刘三阳 王雷
机构地区 西安电子科技大学理学院 空军工程大学理学院
出处 《西北大学学报（自然科学版）》 CAS CSCD 北大核心 2006年第6期871-874,共4页 Journal of Northwest University（Natural Science Edition）
基金 国家自然科学基金资助项目(60573040)
关键词 自正交码 Griesmer界 最优码 拟最优码 self-orthogonal code Griesmer bound optimal code near optimal code
分类号 O157.4 [理学—基础数学] TN919.3 [电子电信—通信与信息系统]
  • 相关文献

参考文献8

  • 1PIEESS V S,HUFFMAIY W C.Handbook of Coding Theory[ M ].Amsterdam:Amsterdam Elsevier,1998.
  • 2CALDERBANK A R,RAINS E M.Quantum error correction via codes over GF(4)[ J ].IEEE Trans Inf Theory,1998,44:1369 -1387.
  • 3HAMADA N.The nonexistence of some quaternary linear codes meeting the Griesmer bound and the bound for N4(5,d)[J].Math Japon,1996,43:7-21.
  • 4李瑞虎.[D].西安:西北工业大学,2004.
  • 5BHANDARI M C,GARG M S.Optimal codes of dimension 3 and 4[J].IEEE Trans Inf Theory,1992,38:1564-1567.
  • 6BOUKLLIEVE L,PATRIC R J.Classification of self-orthogonal codes over and[ J ].Society for Industrial and Applied Mathematics,2005,19(2):363-370.
  • 7马月娜,赵学军,冯有前.F_4上2维和3维的最优自正交码[J].空军工程大学学报（自然科学版）,2005,6(5):63-66. 被引量：5
  • 8余江明,李志慧.利用伪辛几何构造新的带仲裁的认证码[J].西北大学学报（自然科学版）,2005,35(1):7-10. 被引量：1

二级参考文献7

  • 1Rains E M, Sloane N J A. Self-dual codes. In Handbook of Coding Theory [M].Netherlands: Elsevier, 1998.
  • 2Calderbank A R, Rains E M.Quantun Error Correction Via Codes Over GF(4) [J]. IEEE Trans. Inf. Theory, 1998,44:1369-1387.
  • 3Brouwer A E. Bound on the Size of Linear Codes. In Handbook of Coding Theory [M].Netherlands: Elsevier, 1998.
  • 4Hamada N. The Nonexistence of Some Quaternary Linear Codes Meeting the Griesmer Bound and the Bound for N4(5,d)[J].Math. Japon. 1996,43:7-21.
  • 5李瑞虎.[D].西安:西北工业大学,2004.
  • 6Bhandari M C, Garg M S. Optimal Codes of Dimension 3 and 4[J].IEEE Trans. Inf. Theory, 1992, 38:1564-1567.
  • 7GAO YOU AND ZOU ZENGJIA (Department of Basic Science, Northeast Institute of Electric Power, Jinn 132012)..TWO　NEW　CONSTRUCTIONS　OF　CARTESIAN　AUTHENTICATION　CODES　FROM　SYMPLECTIC　GEOMETRY[J].Applied Mathematics(A Journal of Chinese Universities),1995,10(3):345-356. 被引量：4

共引文献13

同被引文献14

  • 1Calderbank A R,Rains E M.Quantum error correction via codes over GF(4)[J].IEEE Trans lnf Theory,1998,44:1369-1387.
  • 2Hamada N.The nonexistence of some quaternary linear codes meeting the Griesmer bound and the bound for N4 (5,d)[J].Math Japon, 1996,43 : 7-21.
  • 3Bhandari M C,Garg M S.Optimal codes of dimension 3 and 4[J]. IEEE Trans Inf Theory, 1992,38:1564-1567.
  • 4Pless V S,Huffman W C.Handbook of coding theory [M].Amsterdam.The Netherlands:Elsevier, 1998: 179-294,295-432.
  • 5Boukllieve Iliya,Otergard Patric R J.Classification of self-orthogonal codes over F3 and F4[J].Society for Industrial and Applied Mathematics, 2005,19 (2) : 363-370.
  • 6李瑞虎.[D].西安:西北工业大学,2004.
  • 7BAARTMANS A,YUEAS J L.Caps in the projective ge-ometry PG(n,4)[J].Finite Fields and Their Applica-tions,2004,10:159-167.
  • 8EDELY,BIERBRAUTERJ.41 is the largest size of a cap in PG (4,4)[J].Designs,Codes and Cryptography,1999,16:151-160.
  • 9EDEL Y,BIERBRAUER J.Caps of order 3q2 in affine 4-space in character 2[J].Finite Fields and Their applica-tions,2004,10:168-182.
  • 10CHEN H.Some good quantum error-correcting codes from algebrie geometric codes[J].IEEE Trans Inf Theory,2001,47:2 059-2 061.

引证文献3

二级引证文献1

西北大学学报（自然科学版）
2006年 第6期

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