Shi, Minjia Li, Shitao Solé, Patrick

We study the codes of the title by the CRT method, that decomposes such codes into constituent codes, which are shorter codes over larger alphabets. Criteria on these constituent codes for self-duality and linear complementary duality of the decomposed codes are derived. The special class of the one-generator codes is given a polynomial representat...

galvez, lucky kim, jon-lark

Practically good error-correcting codes should have good parameters and efficient decoding algorithms. Some algebraically defined good codes, such as cyclic codes, Reed&ndash / Solomon codes, and Reed&ndash / Muller codes, have nice decoding algorithms. However, many optimal linear codes do not have an efficient decoding algorithm except for the ge...

choi, whan-hyuk

The purpose of this paper is to classify and enumerate self-dual codes of length 6 over finite field Z p . First, we classify these codes into three cases: decomposable, indecomposable non-MDS and MDS codes. Then, we complete the classification of non-MDS self-dual codes of length 6 over Z p for all primes p in terms of their automorphism group. We...

han, sunghyu

In this study, we explore maximum distance separable (MDS) self-dual codes over Galois rings G R ( p m , r ) with p &equiv / &minus / 1 ( mod 4 ) and odd r. Using the building-up construction, we construct MDS self-dual codes of length four and eight over G R ( p m , 3 ) with ( p = 3 and m = 2 , 3 , 4 , 5 , 6 ), ( p = 7 and m = 2 , 3 ), ( p = 11 an...

Huang, Daitao Shi, Minjia Sole, Patrick

We study double circulant LCD codes over Z p 2 for all odd primes p, and self-dual double circulant codes over Z p 2 for primes p ≡ 1 (mod 4). We derive exact enumeration formu-lae, and asymptotic lower bounds on the minimum distance of the p-ary images of these codes by the classical Gray maps.

Shi, Minjia Huang, Daitao Sok, Lin Sole, Patrick

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 ≡ 3 (mod 4), we give an algorithm to construct a duality preserving bijective Gray map from such a Galois ring to Z 2 p 2. Using random coding, w...

han, sunghyu

Binary self-dual codes and additive self-dual codes over GF(4) contain common points. Both have Type I codes and Type II codes, as well as shadow codes. In this paper, we provide a comprehensive description of extremal and near-extremal Type I codes over GF(2) and GF(4) with minimal shadow. In particular, we prove that there is no near-extremal Typ...

Raka, Madhu
Published in
Indian Journal of Pure and Applied Mathematics

Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{F}_q$$\end{document} be a finite field with q = pm elements, where p is any prime and m ≥ 1. In this paper, ...

Gutiérrez García, Ismael Villar Salinas, Darwin

In this article we present some techniques to determine the types of automorphisms of extremal doubly even binary self-dual codes, also called extremal type II codes, with parameters [24, 12, 8], [48, 24, 12] and [120, 60, 24]. We aim to obtain information about the automorphism group considering the exclusion of some prime numbers from its order. ...

Aguilar Melchor, Carlos Gaborit, Philippe Kim, Jon-Lark Sok, Lin Solé, Patrick

In this paper we classify all extremal and s-extremal binary self-dual codes of length 38. There are exactly 2744 ex- tremal [38, 19, 8] self-dual codes, two s-extremal [38, 19, 6] codes, and 1730 s-extremal [38, 19, 8] codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual cod...