Binary codes from reflexive uniform subset graphs on $3$-sets

Washiela Fish; Jennifer D. Key; Eric Mwambene

doi:10.3934/amc.2015.9.211

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2015, Volume 9, Issue 2: 211-232. Doi: 10.3934/amc.2015.9.211

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Binary codes from reflexive uniform subset graphs on $3$-sets

1.
Department of Mathematics and Applied Mathematics, University of the Western Cape, 7535 Bellville

Received: February 28, 2014

Published: April 2015

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Abstract

We examine the binary codes $C_2(A_i+I)$ from matrices $A_i+I$ where $A_i$ is an adjacency matrix of a uniform subset graph $\Gamma(n,3,i)$ of $3$-subsets of a set of size $n$ with adjacency defined by subsets meeting in $i$ elements of $\Omega$, where $0 \le i \le 2$. Most of the main parameters are obtained; the hulls, the duals, and other subcodes of the $C_2(A_i+I)$ are also examined. We obtain partial PD-sets for some of the codes, for permutation decoding.

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Mathematics Subject Classification: Primary: 05C45, 05B05; Secondary: 94B05.

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