The second weight of generalized Reed-Muller codes in most cases

Details The second weight of generalized Reed-Muller codes in most cases The second weight of generalized Reed-Muller codes in most cases

2009-02-01

arxiv.org/abs/0902.0058v2

Computer Science

Information Theory

This version corrects minor misprints and gives a more detailed proof of a combinatorial lemma

Scientific paper

The second weight of the Generalized Reed-Muller code of order $d$ over the
finite field with $q$ elements is now known for $d (n-1)(q-1)$. In
this paper, we determine the second weight for the other values of $d$ which
are not multiple of $q-1$ plus 1. For the special case $d=a(q-1)+1$ we give an
estimate.

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