On the second weight of generalized Reed-Muller codes

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Abstract

Not much is known about theweight distribution of the generalized Reed-Muller code RMq (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 +1--1-1weights. For the case = 2 the second weight is now known for all values of s. The results are derived mainly by using Gröbner basis theoretical methods.
Original languageEnglish
JournalDesigns, Codes and Cryptography
Volume48
Issue number3
Pages (from-to)323-330
Number of pages8
ISSN0925-1022
DOIs
Publication statusPublished - 2008

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