Related papers: New extremal binary self-dual codes from a modifie…
Currently, the existence of an extremal singly even self-dual code of length $24k+10$ is unknown for all nonnegative integers $k$. In this note, we study singly even self-dual $[24k+10,12k+5,4k+2]$ codes. We give some restrictions on the…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
A binary linear code whose permutation automorphism group has a fixed point free permutation of order $3$ is called a binary cubic code. The scope of this paper is to investigate the structural properties of binary cubic codes. Let $C$ be a…
We show that there are good long binary generalized quasi-cyclic self-dual (either Type I or Type II) codes.
In this paper, we propose a sufficient condition for a family of 2-generator self-orthogonal quasi-cyclic codes with respect to Hermitian inner product. Supported in the Hermitian construction, we show algebraic constructions of good…
In this note, we complete the classification of extremal doubly even self-dual codes with 2-transitive automorphism groups.
In the last 60 years coding theory has been studied a lot over finite fields $\mathbb{F}_q$ or commutative rings $\mathcal{R}$ with unity. Although in $1993$, a study on the classification of the rings (not necessarily commutative or ring…
This paper investigates the existence, enumeration and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic $p^2$ and order $p^4$ with $p$ and odd prime. When $p \equiv 3 \pmod{4},$ we give…
In 2002, Tonchev first constructed some linear binary codes defined by the adjacency matrices of undirected graphs. So, graph is an important tool for searching optimum codes. In this paper, we introduce a new method of searching (proposed)…
Binary cyclic codes are worth studying due to their applications and theoretical importance. It is an important problem to construct an infinite family of cyclic codes with large minimum distance $d$ and dual distance $d^{\perp}$. In recent…
Binary optimal codes often contain optimal or near-optimal subcodes. In this paper we show that this is true for the family of self-dual codes. One approach is to compute the optimum distance profiles (ODPs) of linear codes, which was…
In this paper, we employ group rings and automorphism groups of binary linear codes to construct new record-breaking binary linear codes. We consider the semidirect product of abelian groups and cyclic groups and use these groups to…
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and…
A Type IV-II Z4-code is a self-dual code over Z4 with the property that all Euclidean weights are divisible by eight and all codewords have even Hamming weight. In this paper we use generalized bent functions for a construction of…
Double negacirculant (DN) codes are the analogues in odd characteristic of double circulant codes. Self-dual DN codes of odd dimension are shown to be consta-dihedral. Exact counting formulae are derived for DN codes. The special class of…
The automorphism group of a binary doubly-even self-dual code is always contained in the alternating group. On the other hand, given a permutation group $G$ of degree $n$ there exists a doubly-even self-dual $G$-invariant code if and only…
The additive codes may have better parameters than linear codes. However, it is still a challenging problem to efficiently construct additive codes that outperform linear codes, especially those with greater distances than linear codes of…
A classification of quaternary Hermitian self-dual codes of length 20 is given. Using this classification, a classification of extremal quaternary Hermitian self-dual codes of length 22 is also given.
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
Binary cyclic codes have been a hot topic for many years, and significant progress has been made in the study of this types of codes. As is well known, it is hard to construct infinite families of binary cyclic codes [n, n+1/2] with good…