DocumentCode
1502255
Title
On some cosets of the first-order Reed-Muller code with high minimum weight
Author
Fontaine, Caroline
Author_Institution
Inst. Nat. de Recherche en Inf. et Autom., Le Chesnay, France
Volume
45
Issue
4
fYear
1999
fDate
5/1/1999 12:00:00 AM
Firstpage
1237
Lastpage
1243
Abstract
We study a family of particular cosets of the first-order Reed-Muller code R(1,m): those generated by special codewords, the idempotents. Thus we obtain new maximal weight distributions of cosets of R(1,7) and 84 distinct almost maximal weight distributions of cosets of R(1,9), that is, with minimum weight 240. This leads to crypotographic applications in the context of stream ciphers
Keywords
Reed-Muller codes; binary codes; cryptography; cyclic codes; binary codes; codewords; cosets; crypotographic applications; cyclic code; first-order Reed-Muller code; high minimum weight; idempotents; maximal weight distributions; stream ciphers; Algebra; Boolean functions; Codes; Cryptography; Galois fields; Information theory; Terminology;
fLanguage
English
Journal_Title
Information Theory, IEEE Transactions on
Publisher
ieee
ISSN
0018-9448
Type
jour
DOI
10.1109/18.761276
Filename
761276
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