Self-orthogonal and self-dual codes constructed via combinatorial designs and Diophantine equations
type: Item
instance of: scholarly article
title: Self-orthogonal and self-dual codes constructed via combinatorial designs and Diophantine equations
zbMATH Open document ID: 1054.94018
published in: Designs, Codes and Cryptography
publication date: 2004-08-16T00:00:00Z
review text: A self-dual code over \(\mathbb{Z}_p\) is a subcode \(C\) of \(\mathbb{Z}_p^n\) with \(C=C^\perp.\) These codes are of great interest from a coding theory perspective and also with respect to their connection with finite designs. Numerous constructions of these codes from combinatorial structures exist in the literature. Orthogonal designs and generalized orthogonal designs can be described as matrices satisfying certain algebraic conditions. In this work the authors generalize some constructions using orthogonal designs, generalized orthogonal designs and Diophantine equations to construct new self-dual and self-orthogonal codes. They construct new self-dual codes of length \(32\) over \(\mathbb{Z}_{11}\) and \(\mathbb{Z}_{13}\) with minimum distance \(12\) which are better than previously known codes for these cases.
reviewed by: Steven T. Dougherty
Mathematics Subject Classification ID: 94B25
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 11D79
Mathematics Subject Classification ID: 94B05
zbMATH DE Number: 2091515
zbMATH Keywords: self-dual codes
zbMATH Keywords: generalized orthogonal designs
zbMATH Keywords: Diophantine equations
zbMATH Keywords: construction
author: Stelios D. Georgiou
author: Christos Koukouvinos
MaRDI profile type: Publication
full work available at URL: b:desi.0000029222.35938.bf
OpenAlex ID: W2077125930
DOI: 10.1023/B:DESI.0000029222.35938.BF
description: scientific article; zbMATH DE number 2091515