The number of inequivalent (2R+3,7)R optimal covering codes

Kéri, Gerzson and Östergard, PRJ (2006) The number of inequivalent (2R+3,7)R optimal covering codes. Journal of Integer Sequences, 9 (4). pp. 1-8.

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Abstract

Let (n,M)R denote any binary code with length n, cardinality M and covering radius R. The classification of (2R+3,7)R codes is settled for any R=1,2,..., and a characterization of these (optimal) codes is obtained. It is shown that, for R=1,2,..., the numbers of inequivalent (2R+3,7)R codes form the sequence 1,3,8,17,33,... identified as A002625 in the Encyclopedia of Integer Sequences and given by the coefficients in the expansion of 1/((1-x)3(1-x2)2(1-x3)).

Item Type: Article
Uncontrolled Keywords: covering radius, classification of codes, integer sequence
Subjects: Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány
Depositing User: Eszter Nagy
Date Deposited: 11 Dec 2012 15:20
Last Modified: 11 Dec 2012 15:20
URI: http://eprints.sztaki.hu/id/eprint/4149

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