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TitleThe second weight of generalized Reed-Muller codes in most cases.
Author(s) Robert Rolland
TypeArticle in Journal
AbstractThe second weight of the Generalized Reed-Muller code of length q n and order d over the finite field with q elements is now known for d&#8201;<&#8201;q and d&#8201;>&#8201;(n&#8201;&#8722;&#8201;1)(q&#8201;&#8722;&#8201;1). In this paper, we determine the second weight for the other values of d which are not multiples of q&#8201;&#8722;&#8201;1 plus 1. For the special case d&#8201;=&#8201;a(q&#8201;&#8722;&#8201;1)&#8201;+&#8201;1 we give an estimate.
KeywordsFinite field, Footprint, Generalized Reed-Muller code, Gröbner basis, Hamming weight, Hypersurface, Second weight, Weight distributio
ISSN1936-2455/e
URL http://link.springer.com/article/10.1007%2Fs12095-009-0014-2
LanguageEnglish
JournalCryptogr. Commun.
Volume2
Number1
Pages19--40
PublisherSpringer US, New York, NY
Year2010
Edition0
Translation No
Refereed No
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