Designs, Codes and Cryptography

, Volume 63, Issue 3, pp 321-330

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

Weight enumeration of codes from finite spaces

  • Relinde P. M. J. JurriusAffiliated withDepartment of Mathematics and Computer Science, Eindhoven University of Technology Email author 


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.


Coding theory Weight enumeration Finite geometry

Mathematics Subject Classification (2000)

05B25 11T71