常循环码的s-Hermitian自对偶码
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摘要
主要研究了常循环码的自对偶码.给出了s-Hermitian自对偶码的定义,并进一步给出了s-Hermitian自对偶常循环码的的充要条件.
This paper is devoted to the study of self-dual codes arising from constacyclic codes. We give the definition of s-Hermitian linear self-dual codes. Necessary and sufficient conditions are given for the existence of s-Hermitian self-dual constacyclic codes over finite fields.
This paper is devoted to the study of self-dual codes arising from constacyclic codes. We give the definition of s-Hermitian linear self-dual codes. Necessary and sufficient conditions are given for the existence of s-Hermitian self-dual constacyclic codes over finite fields.
引文
[1]Kim J L,Lee Y.Euclidean and Hermitian self-dual MDS codes over large finite fields[J].Journal of Combinatorial Theory,Series A,2004,105(1):79-95.
[2]Blackford T.Negacyclic duadic codes[J].Finite Fields and Their Applications,2008,14(4):930-943.
[3]Pless V.A classification of self-orthogonal codes over F_2[J].Discrete Mathematics,1972,3:209-246.
[4]Guenda K.New MDS self-dual codes over large finite fields[J].Designs,Codes and Cryptography,2012,62(1):31-42.
[5]Yang J S,Cai W C.On self-dual constacyclic codes over finite fields[J].Designs,Codes and Cryptography,2015,74(2):355-364.
[6]Gulliver T A,Kim J L,Lee Y.New MDS or near MDS self-dual codes[J].Institute of Electronics Engineers Transactions on Information Theory,2008,54(9):4354-4360.
[7]Pedersen P,Dahl C.Classification of pseudo-cyclic MDS codes[J].Institute of Electrical and Electronics Engineers Transactions on Information Theory,1991,37(2):365-370.
[8]Vant Lint J H.Introduction to Coding Theory[M].3rd ed.Berlin/Heidelberg,Germany:Springer-Verlag,2003.
[9]Dinh H Q.Constacyclic codes of length p~s over F_(p~m)+uF_(p~m)[J].Journal of Algebra,2010,324(5):940-950.
[2]Blackford T.Negacyclic duadic codes[J].Finite Fields and Their Applications,2008,14(4):930-943.
[3]Pless V.A classification of self-orthogonal codes over F_2[J].Discrete Mathematics,1972,3:209-246.
[4]Guenda K.New MDS self-dual codes over large finite fields[J].Designs,Codes and Cryptography,2012,62(1):31-42.
[5]Yang J S,Cai W C.On self-dual constacyclic codes over finite fields[J].Designs,Codes and Cryptography,2015,74(2):355-364.
[6]Gulliver T A,Kim J L,Lee Y.New MDS or near MDS self-dual codes[J].Institute of Electronics Engineers Transactions on Information Theory,2008,54(9):4354-4360.
[7]Pedersen P,Dahl C.Classification of pseudo-cyclic MDS codes[J].Institute of Electrical and Electronics Engineers Transactions on Information Theory,1991,37(2):365-370.
[8]Vant Lint J H.Introduction to Coding Theory[M].3rd ed.Berlin/Heidelberg,Germany:Springer-Verlag,2003.
[9]Dinh H Q.Constacyclic codes of length p~s over F_(p~m)+uF_(p~m)[J].Journal of Algebra,2010,324(5):940-950.