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TitleOn the second weight of generalized Reed-Muller codes.
Author(s) Olav Geil
TypeArticle in Journal
AbstractNot 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)(q1) 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.
KeywordsFootprint, Generalized Reed-Muller code, Gröbner basis
ISSN0925-1022; 1573-7586/e
URL http://link.springer.com/article/10.1007%2Fs10623-008-9211-9
LanguageEnglish
JournalDes. Codes Cryptography
Volume48
Number3
Pages323--330
PublisherSpringer US, New York, NY
Year2008
Edition0
Translation No
Refereed No
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