Weight enumeration of codes from finite spaces
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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.
KeywordsCoding theory Weight enumeration Finite geometry
Mathematics Subject Classification (2000)05B25 11T71
The author would like to thank Vladimir Tonchev for coming up with the question about the weight enumerator of the extension codes of the Simplex code, and for his encouraging conversations on the subject.
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