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
fDate :
5/1/1999 12:00:00 AM
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;
Journal_Title :
Information Theory, IEEE Transactions on
