Designs, Codes and Cryptography

, Volume 48, Issue 3, pp 323–330 | Cite as

On the second weight of generalized Reed-Muller codes



Not much is known about the weight distribution of the generalized Reed-Muller code RM q (s,m) when q > 2, s > 2 and m ≥ 2. Even the second weight is only known for values of s being smaller than or equal to q/2. In this paper we establish the second weight for values of s being smaller than q. For s greater than (m – 1)(q – 1) we then find the first s + 1 – (m – 1)(q–1) weights. For the case m = 2 the second weight is now known for all values of s. The results are derived mainly by using Gröbner basis theoretical methods.


Footprint Generalized Reed-Muller code Gröbner basis Hamming weight Weight distribution 

AMS classifications

11G25 11T71 12.25 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesAalborg UniversityAalborgDenmark

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