Related papers: Binary LCD Codes and Self-orthogonal Codes via Sim…
In the field of algebraic geometric codes (AG codes), the characterization of dual codes has long been a challenging problem which relies on differentials. In this paper, we provide some descriptions for certain differentials utilizing…
If C is a binary linear code, let C^2 be the linear code spanned by intersections of pairs of codewords of C. We construct an asymptotically good family of binary linear codes such that, for C ranging in this family, the C^2 also form an…
Linear complementary dual codes (LCD) are linear codes satisfying $C\cap C^{\perp}=\{0\}$. Under suitable conditions, matrix-product codes that are complementary dual codes are characterized. We construct LCD codes using quasi-orthogonal…
Based on cyclic and consta-cyclic simplex codes, a new explicit construction of a family of two-weight codes is presented. These two-weight codes obtained are in the form of 2-generator quasi-cyclic, or quasi-twisted structure. Based on…
We address the maximum size of binary codes and binary constant weight codes with few distances. Previous works established a number of bounds for these quantities as well as the exact values for a range of small code lengths. As our main…
Bazzi and Mitter [3] showed that binary dihedral group codes are asymptotically good. In this paper we prove that the dihedral group codes over any finite field with good mathematical properties are asymptotically good. If the…
This paper explores extremal self-dual double circulant (DC) codes and linear complementary dual (LCD) codes of arbitrary length over the Galois field $\mathbb F_2$. We establish the sufficient and necessary conditions for DC codes and…
In the 2017 paper by Dougherty, Kim, Ozkaya, Sok, and Sol\'e about the linear programming bound for LCD codes the notion $\mathrm{LCD}[n,k]$ was defined for binary LCD $[n,k]$-codes. We find the formula for $\mathrm{LCD}[n,2]$.
Reading channels where $b$-tuples of adjacent symbols are read at every step have e.g.\ applications in storage. Corresponding bounds and constructions of codes for the $b$-symbol metric, especially the pair-symbol metric where $b=2$, were…
The aim of this work is to study the structure and properties of the binary LCD codes having an automorphisms of odd prime order and to present a method for their construction.
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…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
In this paper, we give algorithms and methods of construction of self-dual codes over finite fields using orthogonal matrices. Randomization in the orthogonal group, and code extension are the main tools. Some optimal, almost MDS, and MDS…
Linear complementary pairs (LCP) of codes play an important role in armoring implementations against side-channel attacks and fault injection attacks. One of the most common ways to construct LCP of codes is to use Euclidean linear…
The hull of a linear code over finite fields is the intersection of the code and its dual, and linear codes with small hulls have applications in computational complexity and information protection. Linear codes with the smallest hull are…
LCD codes are linear codes with important cryptographic applications. Recently, a method has been presented to transform any linear code into an LCD code with the same parameters when it is supported on a finite field with cardinality…
In this paper, we give a new method for constructing LCD codes. We employ group rings and a well known map that sends group ring elements to a subring of the $n \times n$ matrices to obtain LCD codes. Our construction method guarantees that…
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…
In recent years, locally repairable codes (LRCs) have attracted considerable attention owing to their pivotal role in distributed storage systems. Since binary linear locally repairable codes can significantly reduce the complexity of both…
In this work, we define a modification of a bordered construction for self-dual codes which utilises $\lambda$-circulant matrices. We provide the necessary conditions for the construction to produce self-dual codes over finite commutative…