On some cosets of the first-order Reed-Muller code
with high minimum weight
INRIA, projet CODES
78153 Le Chesnay Cedex, France
IEEE Transactions on Information Theory, 45(4):1237-1243, 1999.
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.
Boolean function, covering radius, idempotent, Reed-Muller code, stream cipher.