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

C. Fontaine
<span title="">1999</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/niovmjummbcwdg4qshgzykkpfu" style="color: black;">IEEE Transactions on Information Theory</a> </i> &nbsp;
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.
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