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Partial permutation decoding for simplex codes

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


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  • [1]

    E. F. Assmus, Jr. and J. D. Key, "Designs and their Codes,'' Cambridge University Press, Cambridge, 1992.


    W. Bosma, J. Cannon and C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput., 24 (1997), 235-265.doi: 10.1006/jsco.1996.0125.


    J. Cannon, A. Steel and G. White, Linear codes over finite fields, in "Handbook of Magma Functions'' (eds. J. Cannon and W. Bosma), Computational Algebra Group, Department of Mathematics, University of Sydney, (2006), 3951-4023; available online at http://magma.maths.usyd.edu.au/magma


    D. M. Gordon, Minimal permutation sets for decoding the binary Golay codes, IEEE Trans. Inform. Theory, 28 (1982), 541-543.doi: 10.1109/TIT.1982.1056504.


    E. V. Gorkunov, The group of permutation automorphisms of a $q$-ary Hamming code, Probl. Inf. Transm., 45 (2009), 309-316.doi: 10.1134/S0032946009040024.


    W. C. Huffman, Codes and groups, in "Handbook of Coding Theory'' (eds. V.S. Pless and W.C. Huffman), Elsevier, Amsterdam, (1998), 1345-1440.


    J. D. Key, T. P. McDonough and V. C. Mavron, Partial permutation decoding for codes from finite planes, European J. Combin., 26 (2005), 665-682.doi: 10.1016/j.ejc.2004.04.007.


    H.-J. Kroll and R. Vincenti, PD-sets related to the codes of some classical varieties, Discrete Math., 301 (2005), 89-105.doi: 10.1016/j.disc.2004.11.020.


    H.-J. Kroll and R. Vincenti, PD-sets for binary RM-codes and the codes related to the Klein quadric and to the Schubert variety of $PG(5,2)$, Discrete Math., 308 (2008), 408-414.doi: 10.1016/j.disc.2006.11.057.


    H.-J. Kroll and R. Vincenti, Antiblocking decoding, Discrete Appl. Math., 158 (2010), 1461-1464.doi: 10.1016/j.dam.2010.04.007.


    H.-J. Kroll and R. Vincenti, How to find small AI-systems for antiblocking decoding, Discrete Math., 312 (2012), 657-665.doi: 10.1016/j.disc.2011.06.014.


    F. J. MacWilliams, Permutation decoding of systematic codes, Bell System Tech. J., 43 (1964), 485-505.


    F. J. MacWilliams and N. J. A. Sloane, "The Theory of Error-Correcting Codes,'' North-Holland, Amsterdam, 1983.


    T. P. McDonough, Private communication, 2012.


    J. Schönheim, On coverings, Pacific J. Math., 14 (1964), 1405-1411.


    J. Wolfmann, A permutation decoding of the $(24,12,8)$ Golay code, IEEE Trans. Inform. Theory, 29 (1983), 748-750.doi: 10.1109/TIT.1983.1056726.

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