Title :
On the Cusick–Cheon Conjecture About Balanced Boolean Functions in the Cosets of the Binary Reed–Muller Code
Author :
Borissov, Yuri L.
Author_Institution :
Inst. of Math. & Inf., Bulgarian Acad. of Sci., Sofia
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 ges (m-1)/2, is proved.
Keywords :
Boolean functions; Reed-Muller codes; binary codes; Cusick-Cheon conjecture; Reed-Muller code; balanced boolean functions; binary codes; Boolean functions; Cryptography; Galois fields; Informatics; Linear code; Mathematics; Polynomials; Upper bound; Vectors; Boolean function; Krawtchouk polynomial; Reed–Muller code; Walsh–Hadamard transform; coset of a linear code;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2008.2008141
