# American Institute of Mathematical Sciences

August  2010, 4(3): 399-404. doi: 10.3934/amc.2010.4.399

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

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

Received  December 2009 Revised  February 2010 Published  August 2010

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.
Citation: Tsonka Baicheva, Iliya Bouyukliev. On the least covering radius of binary linear codes of dimension 6. Advances in Mathematics of Communications, 2010, 4 (3) : 399-404. doi: 10.3934/amc.2010.4.399
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