自对偶码的构造
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摘要
自对偶码是一类非常重要的线性码,构造这类码的方法非常多,文中将给出一种新的构造方法.通过这种构造方法,可以得到许多参数很好的自对偶码.
Self-dual codes are an important class of linear codes. There are many constructions of self-dual codes. In this paper, we give a new construction of selfdual codes. It turns out that many new good self-dual codes with large code length are obtained from the construction.
Self-dual codes are an important class of linear codes. There are many constructions of self-dual codes. In this paper, we give a new construction of selfdual codes. It turns out that many new good self-dual codes with large code length are obtained from the construction.
引文
[1]Rains E,Sloane N J A.Self-dual codes[M]//Pless V,Huffman W.Handbook of Coding Theory,Amsterdam/The Netherlands:Elsevier,1998.
[2]Gulliver T A,Harada M.Classification of extremal double circulant self-dual codes of lengths64 to 72[J].Designs,Codes and Cryptography,1998,13:257-269.
[3]Zhang S Y.On the nonexistence of extremal self-dual codes[J].Discrete Applied Mathematics,1999,91:277-286.
[4]Huffman W C.Decomposing and shortening codes using automorphisms[J].IEEE Trans Inform Theory,1986,32(6):833-836.
[5]Betsumiya K,Georgiou S,Gulliver T A,Harada M,Koukouvinos C.On self-dual codes over some prime fields[J].Discrete Math,2003,262:37-58.
[6]Bouyuklieva S.On the automorphism group of a doubly-even(72,36,16)code[J].IEEE Trans Inform Theory,2004,50(3):544-547.
[7]Bouyuklieva S.On the automorphisms of order 2 with fixed points for the extremal self-dual codes of length 24 m[J].Designs,Codes and Cryptography,2002,25:5-13.
[8]Bouyuklieva S,Russeva R,Yankov N.On the structure of binary self-dual codes having an automorphism of order a square of an odd prime[J].IEEE Trans Inform Theory,2005,51(10):3678-3686.
[9]Dontcheva R A.On the doubly-even self-dual codes of length 96[J].IEEE Trans Inform Theory,2002,48(2):557-561.
[10]Dontcheva R A,van Zanten A J,Dodunekov S M.Binary self-dual codes with automorphisms of composite order[J].IEEE Trans Inform Theory,2004,50(2):311-318.
[11]Harada M,Munemasa A.There exists no self-dual[24;12;10]code over F5[J].Designs,Codes and Cryptography,2009,52:125-127.
[12]Yorgova R A.On binary self-dual codes with automorphisms[J].IEEE Trans Inform Theory,2008,54(7):3345-3351.
[13]Voss C,Hoholdt T.An explicit construction of a sequence of codes attaining the TsfasmanVlǎdut-Zink bound:the first step[J].IEEE Trans Inform Theory,1997,43(1):128-135
[14]Stichtenoth H.Algebraic Function Fields and Codes[M].Berlin:Springer-Verlag,1993.
[15]Lidl R,Niederraiter H.Finite Fields[M].Cambridge:Cambridge University Press,1997.
[16]Grassl M.Codes Tables:Bounds on the Parameters of Various Types of Codes[EB/OL].[2015-01-29].http://www.codetables.de.
[2]Gulliver T A,Harada M.Classification of extremal double circulant self-dual codes of lengths64 to 72[J].Designs,Codes and Cryptography,1998,13:257-269.
[3]Zhang S Y.On the nonexistence of extremal self-dual codes[J].Discrete Applied Mathematics,1999,91:277-286.
[4]Huffman W C.Decomposing and shortening codes using automorphisms[J].IEEE Trans Inform Theory,1986,32(6):833-836.
[5]Betsumiya K,Georgiou S,Gulliver T A,Harada M,Koukouvinos C.On self-dual codes over some prime fields[J].Discrete Math,2003,262:37-58.
[6]Bouyuklieva S.On the automorphism group of a doubly-even(72,36,16)code[J].IEEE Trans Inform Theory,2004,50(3):544-547.
[7]Bouyuklieva S.On the automorphisms of order 2 with fixed points for the extremal self-dual codes of length 24 m[J].Designs,Codes and Cryptography,2002,25:5-13.
[8]Bouyuklieva S,Russeva R,Yankov N.On the structure of binary self-dual codes having an automorphism of order a square of an odd prime[J].IEEE Trans Inform Theory,2005,51(10):3678-3686.
[9]Dontcheva R A.On the doubly-even self-dual codes of length 96[J].IEEE Trans Inform Theory,2002,48(2):557-561.
[10]Dontcheva R A,van Zanten A J,Dodunekov S M.Binary self-dual codes with automorphisms of composite order[J].IEEE Trans Inform Theory,2004,50(2):311-318.
[11]Harada M,Munemasa A.There exists no self-dual[24;12;10]code over F5[J].Designs,Codes and Cryptography,2009,52:125-127.
[12]Yorgova R A.On binary self-dual codes with automorphisms[J].IEEE Trans Inform Theory,2008,54(7):3345-3351.
[13]Voss C,Hoholdt T.An explicit construction of a sequence of codes attaining the TsfasmanVlǎdut-Zink bound:the first step[J].IEEE Trans Inform Theory,1997,43(1):128-135
[14]Stichtenoth H.Algebraic Function Fields and Codes[M].Berlin:Springer-Verlag,1993.
[15]Lidl R,Niederraiter H.Finite Fields[M].Cambridge:Cambridge University Press,1997.
[16]Grassl M.Codes Tables:Bounds on the Parameters of Various Types of Codes[EB/OL].[2015-01-29].http://www.codetables.de.