Weight enumeration of codes from finite spaces
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- Jurrius, R.P.M.J. Des. Codes Cryptogr. (2012) 63: 321. doi:10.1007/s10623-011-9557-2
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.