The weight distributions of constacyclic codes

Abstract

Let Fq be a finite field with q elements. Suppose that a, λ ∈ F * q , a n = λ with n|(q − 1). In this paper, we determine the weight distribution of a class of λ-constacyclic codes of length nm with the parity check polynomial h(x) = (x m − aξ st )(x m − aξ s(t+1) ) . . . (x m − aξ s(t+r−1) ) and n > (r − 1)m, where s, t, r are positive integers and ξ ∈ Fq is a primitive n-th root of unity. Moreover, we give the weight distributions of λ-constacyclic codes of length nm explicitly in several cases: (1) r = 1, n > 1; (2) r = 2, m = 2 and n > 2;(3) r = 2, m = 3 and n > 3; (4) r = 3, m = 2 and n > 4.

A class of narrow-sense BCH codes over $$\mathbb {F}_q$$ of length $$\frac{q^m-1}{2}$$

“…In [9], [26], [32], [33], the authors studied the parameters of negacyclic BCH codes of length n = q 2m −1 2 , q m +1 2 , q m −1 4 and q m −1 2λ respectively. In [11], [17], [20], the authors gave some researches about weight distributions. There are many results on the dimension and the minimum distance in [4], [6], [13], [31].…”