Related papers: Constructions of binary self-orthogonal singly-eve…
This paper examines linear binary codes capable of correcting one or more errors. For the single-error-correcting case, it is shown that the Hamming bound is achieved by a constructive method, and an exact expression for the minimal…
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…
The main purpose of this paper is to further study the structure, parameters and constructions of the recently introduced minimal codes in the sum-rank metric. These objects form a bridge between the classical minimal codes in the Hamming…
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…
Binary constant weight codes have important applications and have been studied for many years. Optimal or near-optimal binary constant weight codes of small lengths have been determined. In this paper we propose a new construction of…
The purpose of this paper is two-fold. First we show that Kim's building-up construction of binary self-dual codes is equivalent to Chinburg-Zhang's Hilbert symbol construction. Second we introduce a $q$-ary version of Chinburg-Zhang's…
Linear codes are widely studied due to their applications in communication, cryptography, quantum codes, distributed storage and many other fields. In this paper, we use the trace and norm functions over finite fields to construct a family…
In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ and their binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$ whose defining sets are the certain subsets of $\mathbb{F}_{2^n}^m$ obtained from…
In this paper, we consider minimal linear codes in a general construction of linear codes from q-ary functions. First, we give the sufficient and necessary condition for codewords to be minimal. Second, as an application, we present four…
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…
Let $k\leq n$ be two positive integers and $q$ a prime power. The basic question in minimal linear codes is to determine if there exists an $[n,k]_q$ minimal linear code. The first objective of this paper is to present a new sufficient and…
We construct new $s$-extremal singly even self-dual codes of minimum weights $8,10,12$ and $14$. We also give tables for the currently known results on the existence of $s$-extremal singly even self-dual codes of minimum weights $8,10,12$…
We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and…
We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes. In particular, when the information rate R=1/2, by our constructive lower bound,…
A linear code is said to be self-orthogonal if it is contained in its dual. Self-orthogonal codes are of interest because of their important applications, such as for constructing linear complementary dual (LCD) codes and quantum codes. In…
In this paper we generalize the construction of binary self-orthogonal codes obtained from weakly self-orthogonal designs described by Tonchev in [12] in order to obtain self-orthogonal codes over an arbitrary field. We extend construction…
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…
In this paper, we present a construction of linear codes over $\f_{2^t}$ from Boolean functions, which is a generalization of Ding's method \cite[Theorem 9]{Ding15}. Based on this construction, we give two classes of linear codes…
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…
It is known that correlation-immune (CI) Boolean functions used in the framework of side-channel attacks need to have low Hamming weights. The supports of CI functions are (equivalently) simple orthogonal arrays when their elements are…