Determining the nonlinearity of a new family of APN functions
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Almost perfect nonlinear power functions on GF(2n): the Welch case
IEEE Transactions on Information Theory
On a conjectured ideal autocorrelation sequence and a related triple-error correcting cyclic code
IEEE Transactions on Information Theory
Finite Fields and Their Applications
On the triple-error-correcting cyclic codes with zero set {1, 2i + 1, 2i + 1}
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
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The binary primitive triple-error-correcting BCH code is a cyclic code of minimum distance d = 7 with generator polynomial having zeros α, α3 and α5 where α is a primitive (2n - 1)-root of unity. The zero set of the code is said to be {1, 3, 5}. In the 1970's Kasami showed that one can construct similar triple-error-correcting codes using zero sets consisting of different triples than the BCH codes. Furthermore, in 2000 Chang et. al. found new triples leading to triple-error-correcting codes. In this paper a new such triple is presented. In addition a new method is presented that may be of interest in finding further such triples. The method is illustrated by giving a new and simpler proof of one of the known Kasami triples {1, 2k + 1, 23k + 1} where n is odd and gcd(k, n) = 1 as well as to find the new triple given by {1, 2k + 1, 22k + 1} for any n where gcd(k, n) = 1.