2016/10/26 by Shixin Zhu, Binbin Pang, Zhonghua Sun
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Coset #Field (mathematics) #Finite Group Theory Research #Finite field #Liquid-crystal display #Modulo #Prime (order theory) #cs.IT #graph theory and CDMA systems #math.IT
paper · pdf · doi:10.1007/s11424-017-6301-7
published as J Syst Sci Complex 31, 1065-1077 (2018)
arxiv created 2016/10/26 · openalex created_date 2016/11/04 · openalex publication_date 2017/11/29 · arxiv updated 2021/01/21 · openalex updated_date 2026/08/05
In this paper, by investigating the factor of the xn+1, we deduce that the structure of the reversible negacyclic code over the finite field \mathbbFq, where q is an odd prime power. Though studying q-cyclotomic cosets modulo 2n, we obtain the parameters of negacyclic BCH code of length n=(q^ℓ+1)/(2) , n=(qm-1)/(2(q-1)) and n=\fracqt⋅2τ-12(qt+1). Some optimal linear codes from negacyclic codes are given. Finally, we discuss a class of MDS LCD negacyclic codes.