Related papers: Constructions of Quasi-Twisted Two-Weight Codes
Up to a new invariant $\mu(b)$, the complete $b$-symbol weight distribution of a particular kind of two-weight irreducible cyclic codes, was recently obtained by Zhu et al. [Des. Codes Cryptogr., 90 (2022) 1113-1125]. The purpose of this…
In this paper, we study self-dual codes over $\mathbb{Z}_2 \times (\mathbb{Z}_2+u\mathbb{Z}_2) $, where $u^2=0$. Three types of self-dual codes are defined. For each type, the possible values $\alpha,\beta$ such that there exists a code…
A self-dual binary linear code is called Type I code if it has singly-even codewords, i.e.~it has codewords with weight divisible by $2.$ The purpose of this paper is to investigate interesting properties of Type I codes of different…
In this paper, several classes of three-weight ternary linear codes from non-weakly regular dual-bent functions are constructed based on a generic construction method. Instead of the whole space, we use the subspaces $B_+(f)$ or $B_-(f)$…
Subspace codes have important applications in random network coding. It is interesting to construct subspace codes with both sizes, and the minimum distances are as large as possible. In particular, cyclic constant dimension subspaces codes…
In this note, an intrinsic description of some families of linear codes with symmetries is given, showing that they can be described more generally as quasi group codes, that is, as linear codes allowing a group of permutation automorphisms…
The structure of a linear block code is pivotal in defining fundamental properties, particularly weight distribution, and code design. In this study, we characterize the Type II structure of polar codewords with weights less than twice the…
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…
We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the non-chain ring $\mathbb{F}_p+u\mathbb{F}_p+v\mathbb{F}_p+uv\mathbb{F}_p,$ where $u^2=0,v^2=0,uv=vu.$ These codes are defined as trace codes. They have the…
We provide a detailed study of the general structure of two-dimensional topological stabilizer quantum error correcting codes, including subsystem codes. Under the sole assumption of translational invariance, we show that all such codes can…
In this paper, we describe a new type of DNA codes over two noncommutative rings $E$ and $F$ of order four with characteristic 2. Our DNA codes are based on quasi self-dual codes over $E$ and $F$. Using quasi self-duality, we can describe…
We present an algorithm that takes a CSS stabilizer code as input, and outputs another CSS stabilizer code such that the stabilizer generators all have weights $O(1)$ and such that $O(1)$ generators act on any given qubit. The number of…
In this manuscript, we construct a class of projective three-weight linear codes and two classes of projective four-weight linear codes over F2 from the defining sets construction, and determine their weight distributions by using additive…
We present a new general construction of MDS codes over a finite field $\mathbb{F}_q$. We describe two explicit subclasses which contain new MDS codes of length at least $q/2$ for all values of $q \ge 11$. Moreover, we show that most of the…
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.…
In this paper, necessary and sufficient conditions for the self-orthogonality of t-generator quasi-cyclic (QC) codes are presented under the Euclidean, Hermitian, and symplectic inner products, respectively. Particularly, by studying the…
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…
Constacyclic codes over finite fields are an important class of linear codes as they contain distance-optimal codes and linear codes with best known parameters. They are interesting in theory and practice, as they have the constacyclic…
Batch codes serve as critical tools for load balancing in distributed storage systems. While numerous constructions exist for specific batch sizes t, current methodologies predominantly rely on code dimension parameters, limiting their…
In this article we present a class of codes with few weights arising from special type of linear sets. We explicitly show the weights of such codes, their weight enumerator and possible choices for their generator matrices. In particular,…