For any odd prime p, a classification of all cyclic and negacyclic codes of length 8ps over Fpm are obtained, which establishes the algebra structures in term of specified polynomial generators of such codes. Among ot...For any odd prime p, a classification of all cyclic and negacyclic codes of length 8ps over Fpm are obtained, which establishes the algebra structures in term of specified polynomial generators of such codes. Among other results, all self-dual negacyclic codes of length 8ps are obtained, and the structures of α-constacyclic and β-constacyclic codes of length 8ps over Fpm are established.展开更多
Negacyclic codes of length 2^(s) over the Galois ring GR(2a,m)are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals<(x+1)^(i)>,0≤i≤2^(s)a,of the chain ring GR(2^(a),m)[x]/<x^(2s)+1>...Negacyclic codes of length 2^(s) over the Galois ring GR(2a,m)are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals<(x+1)^(i)>,0≤i≤2^(s)a,of the chain ring GR(2^(a),m)[x]/<x^(2s)+1>.This structure is used to obtain the symbol-pair distances of all such negacyclic codes.Among others,for the special case when the alphabet is the finite field F2m(i.e.,a=1),the symbol-pair distance distribution of constacyclic codes over F2m verifies the Singleton bound for such symbol-pair codes,and provides all maximum distance separable symbol-pair constacyclic codes of length 2^(s) over F_(2m).展开更多
In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m ＋ uFp^m, where p is an odd prime. On the basis of the works of Dinh （in J.Algebra 324,940-950,2010）, we use the Chinese...In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m ＋ uFp^m, where p is an odd prime. On the basis of the works of Dinh （in J.Algebra 324,940-950,2010）, we use the Chinese Remainder Theorem to establish the algebraic structure of cyclic and negacyclic codes of length 2p^s over the ring Fp^m ＋ uFp^m in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes.展开更多
We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or ...We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R.Moreover,we discuss possible extension of our results in the more general setting ofδR-dual skew constacyclic codes over R,whereδR is an automorphism of R.展开更多
基金Supported by the Natural Science Foundation of Hubei Province(D20144401)the Natural Science Foundation of Hubei Polytechnic University(12xjz14A)
文摘For any odd prime p, a classification of all cyclic and negacyclic codes of length 8ps over Fpm are obtained, which establishes the algebra structures in term of specified polynomial generators of such codes. Among other results, all self-dual negacyclic codes of length 8ps are obtained, and the structures of α-constacyclic and β-constacyclic codes of length 8ps over Fpm are established.
文摘Negacyclic codes of length 2^(s) over the Galois ring GR(2a,m)are linearly ordered under set-theoretic inclusion,i.e.,they are the ideals<(x+1)^(i)>,0≤i≤2^(s)a,of the chain ring GR(2^(a),m)[x]/<x^(2s)+1>.This structure is used to obtain the symbol-pair distances of all such negacyclic codes.Among others,for the special case when the alphabet is the finite field F2m(i.e.,a=1),the symbol-pair distance distribution of constacyclic codes over F2m verifies the Singleton bound for such symbol-pair codes,and provides all maximum distance separable symbol-pair constacyclic codes of length 2^(s) over F_(2m).
基金supported by the Natural ScienceFoundation of Hubei Province(D2014401)the Natural Science Foundation of Hubei Polytechnic University(12xjz14A)
文摘In this article, we focus on cyclic and negacyclic codes of length 2p^s over the ring R = Fp^m ＋ uFp^m, where p is an odd prime. On the basis of the works of Dinh （in J.Algebra 324,940-950,2010）, we use the Chinese Remainder Theorem to establish the algebraic structure of cyclic and negacyclic codes of length 2p^s over the ring Fp^m ＋ uFp^m in terms of polynomial generators. Furthermore, we obtain the number of codewords in each of those cyclic and negacyclic codes.
基金This work was supported by the Ministry of Education and Training of Vietnam(Thai Nguyen University)under Grant No.B2019-TNA-02.
文摘We study skew cyclic codes over a class of rings R=F0■F1■⋯■Ft−1,where each Fi(i=0,…,t−1)is a finite field.We prove that a skew cyclic code of arbitrary length over R is equivalent to either a usual cyclic code or a quasi-cyclic code over R.Moreover,we discuss possible extension of our results in the more general setting ofδR-dual skew constacyclic codes over R,whereδR is an automorphism of R.
