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The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the generalized Hamming weights of three classes of linear codes constructed through defining sets and determine them partly for some cases. Particularly, in the semiprimitive case we solve an problem left in Yang et al. (IEEE Trans. Inf. Theory 61(9): 4905--4913, 2015).
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, a class of $q$-ary linear codes with few weights are presented and their weight distributions are determined using Gauss periods. Some of the linea
In this paper, we first introduce the notion of generalized $b$-weights of $[n,k]$-linear codes over finite fields, and obtain some basic properties and bounds of generalized $b$-weights of linear codes which is called Singleton bound for generalized
Let $G$ be a connected graph and let $mathbb{X}$ be the set of projective points defined by the column vectors of the incidence matrix of $G$ over a field $K$ of any characteristic. We determine the generalized Hamming weights of the Reed--Muller-typ
In this paper, we apply two-to-one functions over $mathbb{F}_{2^n}$ in two generic constructions of binary linear codes. We consider two-to-one functions in two forms: (1) generalized quadratic functions; and (2) $left(x^{2^t}+xright)^e$ with $gcd(t,
Let $p$ be a prime and let $q$ be a power of $p$. In this paper, by using generalized Reed-Solomon (GRS for short) codes and extended GRS codes, we construct two new classes of quantum maximum-distance- separable (MDS) codes with parameters [ [[tq, t