On the least covering radius of binary linear codes of dimension 6

Tsonka Baicheva; Iliya Bouyukliev

doi:10.3934/amc.2010.4.399

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2010, Volume 4, Issue 3: 399-404. Doi: 10.3934/amc.2010.4.399

This issue Previous Article Attribute-based group key establishment Next Article LDPC codes associated with linear representations of geometries

On the least covering radius of binary linear codes of dimension 6

Tsonka Baicheva^1, and
Iliya Bouyukliev^1,

1.
Institute of Mathematics and Informatics, BAS, Bulgarian Academy of Sciences, P.O.Box 323, 5000 Veliko Tarnovo

Received: November 30, 2009

Revised: January 31, 2010

Published: July 2010

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Abstract

In this work the least covering radii of all binary linear codes of dimension 6 are determined. Codes of dimension up to 6 and lengths up to 15 having the least covering radius are classified and constructions of codes with $R=t$₂$[n,k]$ of every length and dimension up to 6 are given. Examples of using this classification for the construction of codes with the least covering radius and dimensions greater than 6 are presented.

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Mathematics Subject Classification: Primary: 94B05.

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