Information sets and partial permutation decoding for codes from finite geometries

Authors:
J. D. Key;T. P. Mcdonough;V. C. Mavron
Affiliations:
Department of Mathematical Sciences, Clemson University, 0-106 Martin Hall, Clemson, SC 29634, USA;Institute of Mathematical and Physical Sciences, University of Wales, Aberystwyth, Ceredigion SY23 3BZ, UK;Institute of Mathematical and Physical Sciences, University of Wales, Aberystwyth, Ceredigion SY23 3BZ, UK
Venue:
Finite Fields and Their Applications
Year:
2006

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Abstract

We determine information sets for the generalized Reed-Muller codes and use these to apply partial permutation decoding to codes from finite geometries over prime fields. We also obtain new bases of minimum-weight vectors for the codes of the designs of points and hyperplanes over prime fields.