Weight distributions of cyclic codes of length tlm

Abstract

a b s t r a c tLet F q be a finite field with q elements, l an odd prime, and t, v positive integers such that l v |(q − 1) and gcd(t, l) = 1. In this paper, we give a combinatorial result and use it to determine the weight distribution of a cyclic code of length tl m with t|(q − 1), which is an open question in . Moreover we compute the weight distributions of cyclic codes of length tl m , where q ≡ 3 (mod 4) and t = 4 or 8.

Weight distributions of all irreducible $μ$-constacyclic codes of length $\ell^n$

“…Note that A 0 = 1 and A i = 0 for all 1 ≤ i < d, where d is the minimum Hamming distance of the code. The weight distributions for irreducible cyclic codes has been studied by many authors (see [3,5,12,14,15,16]).…”

“…Over the last few decades, much has been written about constacyclic codes [1,4,6,8,11]. In [16], Zhu et al obtained the weight distribution of a class of cyclic codes of length ℓ m , where ℓ is a prime satisfying that ℓ v ||(q −1) and v is a positive integer, and that 4|(q −1) if ℓ = 2. Chen et al [4] introduced an equivalence relation, called isometry, to classify constacyclic codes over finite fields.…”