On some cosets of the first-order Reed-Muller code
with high minimum weight


Caroline Fontaine
INRIA, projet CODES
BP 105
78153 Le Chesnay Cedex, France
Caroline.Fontaine@inria.fr

IEEE Transactions on Information Theory, 45(4):1237-1243, 1999.

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 cryptographic applications in the context of stream ciphers.

Keywords

Boolean function, covering radius, idempotent, Reed-Muller code, stream cipher.