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
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.