Related papers: A new approach to construct minimal linear codes o…
Partial spread is important in finite geometry and can be used to construct linear codes. From the results in (Designs, Codes and Cryptography 90:1-15, 2022) by Xia Li, Qin Yue and Deng Tang, we know that if the number of the elements in a…
We provide new families of minimal codes in any characteristic. Also, an inductive construction of minimal codes is presented.
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
There are exactly two non-commutative rings of size $4$, namely, $E = \langle a, b ~\vert ~ 2a = 2b = 0, a^2 = a, b^2 = b, ab= a, ba = b\rangle$ and its opposite ring $F$. These rings are non-unital. A subset $D$ of $E^m$ is defined with…
Linear codes with a few weights are an important class of codes in coding theory and have attracted a lot of attention. In this paper, we present several constructions of $q$-ary linear codes with two or three weights from vectorial…
Blocking sets and minimal codes have been studied for many years in projective geometry and coding theory. In this paper, we provide a new lower bound on the size of $t$-fold $s$-blocking sets without the condition $t \leq q$, which is…
Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, linear codes…
Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…
A linear code of length $n$ over a finite chain ring $R$ with residue field $\F_q$ is a $R$-submodule of $R^n$. A $R$-linear code is a code over $\F_q$ (not necessarily linear) which is the generalized Gray map image of a linear code over…
Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…
We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords…
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…
Linear codes have been an interesting subject of study for many years, as linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, a class of…
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, monomials and trinomials over…
In this paper, several infinite families of codes over the extension of non-unital non-commutative rings are constructed utilizing general simplicial complexes. Thanks to the special structure of the defining sets, the principal parameters…
We construct new linear codes with high minimum distance d. In at least 12 cases these codes improve the minimum distance of the previously known best linear codes for fixed parameters n,k. Among these new codes there is an optimal ternary…
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.…
We introduce two constructions of additive codes over finite fields. Both constructions start with a linear code over a field with $q$ elements and give additive codes over the field with $q^h$ elements whose minimum distance is…
We develop three approaches of combinatorial flavour to study the structure of minimal codes and cutting blocking sets in finite geometry, each of which has a particular application. The first approach uses techniques from algebraic…
Minimal codes are a class of linear codes which gained interest in the last years, thanks to their connections to secret sharing schemes. In this paper we provide the weight distribution and the parameters of families of minimal codes…