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Recently, linear codes constructed from defining sets have been studied extensively. They may have nice parameters if the defining set is chosen properly. Let $ m >2$ be a positive integer. For an odd prime $ p $, let $ r=p^m $ and…
Cyclic codes are an interesting subclass of linear codes and have been used in consumer electronics, data transmission technologies, broadcast systems, and computer applications due to their efficient encoding and decoding algorithms. In…
Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first…
Linear codes have been an interesting subject of study for many years. Recently, linear codes with few weights have been constructed and extensively studied. In this paper, for an odd prime p, a class of three-weight linear codes over Fp…
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.…
Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation…
The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…
A new construction of codes from old ones is considered, it is an extension of the matrix-product construction. Several linear codes that improve the parameters of the known ones are presented.
Linear codes with a few weights have wide applications in information security, data storage systems, consuming electronics and communication systems. Construction of the linear codes with a few weights and determination of their parameters…
In this paper, based on the theory of defining sets, two classes of at most six-weight linear codes over $\mathbb{F}_p$ are constructed. The weight distributions of the linear codes are determined by means of Gaussian period and Weil sums.…
In this paper, a class of two-weight and three-weight linear codes over $\gf(p)$ is constructed, and their application in secret sharing is investigated. Some of the linear codes obtained are optimal in the sense that they meet certain…
A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…
Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…
Linear codes with few weights have significant applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. There are a number of methods to construct linear codes, one of which is based on…
A construction is presented that allows to produce subspace codes of long length using subspace codes of shorter length in combination with a rank metric code. The subspace distance of the resulting code, called linkage code, is as good as…
In this paper, based on the theory of defining sets, two classes of five-weight or six-weight linear codes over Fp are constructed. The weight distributions of the linear codes are determined by means of Weil sums and a new type of…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
A large family of linear codes with flexible parameters from almost bent functions and perfect nonlinear functions are constructed and their parameters are determined. Some constructed linear codes and their related codes are optimal in the…
Constacyclic codes are important classes of linear codes that have been applied to the construction of quantum codes. Six new families of asymmetric quantum codes derived from constacyclic codes are constructed in this paper. Moreover, the…
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, almost perfect nonlinear…