Related papers: Linear Codes With Two or Three Weights From Some F…
Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many…
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) $\left(x^{2^t}+x\right)^e$…
Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…
Recently, linear codes constructed by defining sets have attracted a lot of study, and many optimal linear codes with a few weights have been produced. The objective of this paper is to present a class of binary linear codes with three…
Recently, linear codes with few weights have been widely studied, since they have applications in data storage systems, communication systems and consumer electronics. In this paper, we present a class of three-weight and five-weight linear…
Linear codes with few weights have applications in data storage systems, secret sharing schemes, and authentication codes. In this paper, some kinds of p-ary linear codes with few weights are constructed by use of the given de ning set,…
The linear codes with a few weights have been applied widely in combinatorial designs, secret sharing, association schemes, authentication codes and strongly regular graphs. In this paper, we first correct an erroneous result about the…
Two-weight linear codes are linear codes in which any nonzero codeword can have only two possible distinct weights. Those in the Hamming metric have proven to be very interesting for their connections with authentication codes, association…
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…
In the past few years, linear codes with few weights and their weight analysis have been widely studied. In this paper, we further investigate a class of two-weight or three-weight linear codes from defining sets and determine their weight…
Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a class of three-weight…
Binary linear codes with good parameters have important applications in secret sharing schemes, authentication codes, association schemes, and consumer electronics and communications. In this paper, we construct several classes of binary…
In this paper, for any odd prime $p$ and an integer $m\ge 3$, several classes of linear codes with $t$-weight $(t=3,5,7)$ are obtained based on some defining sets, and then their complete weight enumerators are determined explicitly by…
Linear codes can be employed to construct authentication codes, which is an interesting area of cryptography. The parameters of the authentication codes depend on the complete weight enumerator of the underlying linear codes. In order to…
Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…
Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime $p$, we propose a class of $p$-ary linear codes by choosing a proper defining set.…
Linear codes with few weights have been a significant area of research in coding theory for many years, due to their applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. Inspired by…
Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…
A generic construction of linear codes over finite fields has recently received a lot of attention, and many one-weight, two-weight and three-weight codes with good error correcting capability have been produced with this generic approach.…
Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…