ﻻ يوجد ملخص باللغة العربية
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 linear codes obtained are optimal or almost optimal with respect to the Griesmer bound. As s applications, these linear codes can be used to construct secret sharing schemes with nice access structures.
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,
Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of linear codes
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
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
We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a~function of the gap to capacity. This res