# American Institute of Mathematical Sciences

May  2015, 9(2): 211-232. doi: 10.3934/amc.2015.9.211

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

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

Received  March 2014 Published  May 2015

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.
Citation: Washiela Fish, Jennifer D. Key, Eric Mwambene. Binary codes from reflexive uniform subset graphs on $3$-sets. Advances in Mathematics of Communications, 2015, 9 (2) : 211-232. doi: 10.3934/amc.2015.9.211
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