On the Cusick-Cheon conjecture about balanced Boolean functions in the cosets of the binary Reed-Muller code

Authors:
Yuri L. Borissov
Affiliations:
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

In this paper, an amplification of the Cusick-Cheon conjecture on balanced Boolean functions in the cosets of the binary Reed-Muller code RM(k,m) of order k and length 2m, in the cases where k = 1 or k ≥ (m-1)/2, is proved.