2014/07/08 by Long Yu, Hongwei Liu, Yu, Long +1
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Cellular Automata and Applications
paper · pdf · doi:10.48550/arxiv.1407.2032
Let m, k be positive integers such that (m)/(gcd(m,k))≥ 3, p be an odd prime and π be a primitive element of \mathbbFpm. Let h1(x) and h2(x) be the minimal polynomials of -π-1 and π-(pk+1)/(2) over \mathbbFp, respectively. In the case of odd (m)/(gcd(m,k)), when k is even, gcd(m,k) is odd or when (k)/(gcd(m,k)) is odd, Zhou et~al. in \citezhou obtained the weight distribution of a class of cyclic codes C over \mathbbFp with parity-check polynomial h1(x)h2(x). In this paper, we further investigate this class of cyclic codes C over \mathbbFp in the rest case of odd (m)/(gcd(m,k)) and the case of even (m)/(gcd(m,k)). Moreover, we determine the weight distribution of cyclic codes C.