, Volume 63, Issue 3, pp 321-330,
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Date: 21 Aug 2011

Weight enumeration of codes from finite spaces

Abstract

We study the generalized and extended weight enumerator of the q-ary Simplex code and the q-ary first order Reed-Muller code. For our calculations we use that these codes correspond to a projective system containing all the points in a finite projective or affine space. As a result from the geometric method we use for the weight enumeration, we also completely determine the set of supports of subcodes and words in an extension code.

Communicated by J. D. Key.