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Advances in Mathematics of Communications (AMC)
 

Partial permutation decoding for simplex codes

Pages: 505 - 516, Volume 6, Issue 4, November 2012      doi:10.3934/amc.2012.6.505

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

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

Received: January 2012;      Revised: May 2012;      Available Online: November 2012.

 References