Partial permutation decoding for simplex codes

Washiela Fish; Jennifer D. Key; Eric Mwambene

doi:10.3934/amc.2012.6.505

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2012, Volume 6, Issue 4: 505-516. Doi: 10.3934/amc.2012.6.505

This issue Previous Article Existence of cyclic self-orthogonal codes: A note on a result of Vera Pless Next Article

Partial permutation decoding for simplex codes

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

Received: December 31, 2011

Revised: April 30, 2012

Published: October 2012

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Abstract

We show how to find $s$-PD-sets of size $s+1$ that satisfy the Gordon-Schönheim bound for partial permutation decoding for the binary simplex codes $\mathcal S_n(\mathbb F_2)$ for all $n \geq 4$, and for all values of $s$ up to $\left\lfloor\frac{2^n-1}{n}\right\rfloor -1$. The construction also applies to the $q$-ary simplex codes $\mathcal S_n(\mathbb F_q)$ for $q>2$, and to $s$-antiblocking information systems of size $s+1$, for $s$ up to $\left\lfloor\frac{(q^n-1)/(q-1)}{n}\right\rfloor -1$ for all $q$.

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

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