Small additive quaternary codes.
type: Item
instance of: scholarly article
title: Small additive quaternary codes.
zbMATH Open document ID: 1046.94012
DOI: 10.1016/S0195-6698(03)00096-9
author: Aart Blokhuis
author: Andries E. Brouwer
published in: European Journal of Combinatorics
publication date: 2004-03-14T00:00:00Z
review text: Consider the additive group \(Q= \mathbb{Z}_2\times \mathbb{Z}_2\). A code with codewords of length \(n\) over \(Q\) is called additive if it is an additive subgroup of \(Q^n\). A code with codewords of length \(n\) over \(Q\) is called optimal when it has the largest possible size for given values of \(n\) and \(d\). In this article, the authors determine the parameters of the optimal additive codes of word length at most 12 over \(Q\), up to two specific sets of parameters. Some of the codes found improve on the best quaternary codes known. This search for optimal additive codes over \(Q\) is equivalent to the search for how many lines it is possible to take in a binary projective space such that any \(t\) are independent, or equivalently, how many lines it is possible to take in a binary projective space such that no hyperplane contains more than \(m\) of them. Here, lines may be repeated, and a line is sometimes the span of two not necessarily distinct points.
Mathematics Subject Classification ID: 94B05
Mathematics Subject Classification ID: 51E20
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 94B27
zbMATH DE Number: 2056151
zbMATH Keywords: optimal codes
zbMATH Keywords: quaternary codes
zbMATH Keywords: lines
reviewed by: Leo Storme
MaRDI profile type: Publication
cites work: Error-correcting codes over an alphabet of four elements
cites work: Self-dual codes over GF(4)
full work available at URL: s0195-6698(03)00096-9
OpenAlex ID: W2056498695
description: scientific article; zbMATH DE number 2056151