All binary linear codes of lengths up to 18 or redundancy up to 10 are normal

Tsonka Baicheva

doi:10.3934/amc.2011.5.681

Article Contents

2011, Volume 5, Issue 4: 681-686. Doi: 10.3934/amc.2011.5.681

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All binary linear codes of lengths up to 18 or redundancy up to 10 are normal

Tsonka Baicheva^1,

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

Received: November 30, 2010

Revised: May 31, 2011

Published: October 2011

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Abstract

We show that all binary codes of lengths 16, 17 and 18, or redundancy 10, are normal. These results have applications in the construction of codes that attain $t[n,k]$, the smallest covering radius of any binary linear code.

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Mathematics Subject Classification: Primary: 94B05.

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