Codes from the incidence matrices and line graphs of Hamming graphs $H^k(n,2)$ for $k \geq 2$

Pages: 373 - 394, Volume 5, Issue 2, May 2011

doi:10.3934/amc.2011.5.373       Abstract        References        Full Text (518.6K)       Related Articles

Jennifer D. Key - Department of Mathematics and Applied Mathematics, University of the Western Cape, 7535 Bellville, South Africa (email)
Washiela Fish - Department of Mathematics and Applied Mathematics, University of the Western Cape, 7535 Bellville, South Africa (email)
Eric Mwambene - Department of Mathematics and Applied Mathematics, University of the Western Cape, 7535 Bellville, South Africa (email)

Abstract: We examine the $p$-ary codes, for any prime $p$, that can be obtained from incidence matrices and line graphs of the Hamming graphs, $H^k(n,m)$, for $k \geq 2$. For $m=2$, we obtain the main parameters of the codes from the incidence matrices, including the minimum weight and the nature of the minimum words. We show that all the codes can be used for full permutation decoding.

Keywords:  Hamming graphs, codes, permutation decoding.
Mathematics Subject Classification:  Primary: 05C45, 94B05; Secondary: 05B05.

Received: May 2010;      Revised: June 2010;      Published: May 2011.

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