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
Abstract We investigate negacyclic codes over the Galois ring GR（2a,m） of length N = 2kn, where n is odd and k≥0. We first determine the structure of u-constacyclic codes of length n over the finite chain ring GR（...Abstract We investigate negacyclic codes over the Galois ring GR（2a,m） of length N = 2kn, where n is odd and k≥0. We first determine the structure of u-constacyclic codes of length n over the finite chain ring GR（2a, m）[u]/〈u2k ＋ 1〉. Then using a ring isomorphism we obtain the structure of negacyclic codes over GR（2a, m） of length N = 2kn （n odd） and explore the existence of self-dual negacyclic codes over GR（2a, m）. A bound for the homogeneous distance of such negacvclic codes is also given.展开更多
This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2n, the authors obtain the parameters of LCD negacycli...This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2n, the authors obtain the parameters of LCD negacyclic codes of lengths n=qt＋1/2,qm-1/2（q-1） and qt·2τ-1/2（q2＋1）respectively. And many optimal codes are given. Moreover, the authors research two special classes of MDS LCD negacyclic codes of length n｜q-1/2 and n｜q＋1/2,respectively.展开更多
The Hamming distances of all negacyclic codes of length 28 over the Gaiois ring GR （2^α, m） are given. In particular, the Lee distances of all negacyclic codes over Z4 of length 2^s are obtained. The Gray images of...The Hamming distances of all negacyclic codes of length 28 over the Gaiois ring GR （2^α, m） are given. In particular, the Lee distances of all negacyclic codes over Z4 of length 2^s are obtained. The Gray images of such negacyclic codes over Z4 are also determined under the Gray map.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, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes...In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained.展开更多
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
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supported by National Natural Science Foundation of China (Grant No. 60973125)College Doctoral Funds of China (Grant No. 20080359003)+1 种基金the Fundamental Research Funds for the Central Universities (Grant No. 2011HGXJ1079)the open research fund of National Mobile Communications Research Laboratory, Southeast University
文摘Abstract We investigate negacyclic codes over the Galois ring GR（2a,m） of length N = 2kn, where n is odd and k≥0. We first determine the structure of u-constacyclic codes of length n over the finite chain ring GR（2a, m）[u]/〈u2k ＋ 1〉. Then using a ring isomorphism we obtain the structure of negacyclic codes over GR（2a, m） of length N = 2kn （n odd） and explore the existence of self-dual negacyclic codes over GR（2a, m）. A bound for the homogeneous distance of such negacvclic codes is also given.
基金supported by the National Natural Science Foundation of China under Grant Nos.61370089,61572168,11501156the Anhui Provincial Natural Science Foundation under Grant No.1508085SQA198
文摘This paper deduces the structure of LCD negacyclic codes over the finite field Fq, where q is an odd prime power. Based on the study of q-cyclotomic cosets modulo 2n, the authors obtain the parameters of LCD negacyclic codes of lengths n=qt＋1/2,qm-1/2（q-1） and qt·2τ-1/2（q2＋1）respectively. And many optimal codes are given. Moreover, the authors research two special classes of MDS LCD negacyclic codes of length n｜q-1/2 and n｜q＋1/2,respectively.
基金the National Natural Science Foundation of China under Grant No.60673074
文摘The Hamming distances of all negacyclic codes of length 28 over the Gaiois ring GR （2^α, m） are given. In particular, the Lee distances of all negacyclic codes over Z4 of length 2^s are obtained. The Gray images of such negacyclic codes over Z4 are also determined under the Gray map.
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 SRF for ROCS,SEM,the Key Project of Chinese Ministry of Education (108099)CCNU Project (CCNU09Y01003)
文摘In this article, cyclic codes and negacyclic codes over formal power series rings are studied. The structure of cyclic codes over this class of rings is given, and the relationship between these codes and cyclic codes over finite chain rings is obtained. Using an isomorphism between cyclic and negacyclic codes over formal power series rings, the structure of negacyclic codes over the formal power series rings is obtained.
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.
