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Determining deep holes is an important open problem in decoding Reed-Solomon codes. It is well known that the received word is trivially a deep hole if the degree of its Lagrange interpolation polynomial equals the dimension of the Reed-Solomon code. For the standard Reed-Solomon codes [p − 1, k]p with p a prime, Cheng and Murray conjectured in 2007 that… (More)

Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [8], we showed that the received word u is a deep hole of the standard Reed-Solomon codes [q − 1, k]q if its Lagrange interpolation polynomial is the sum of monomial of degree q − 2 and a polynomial of degree at most k − 1. In this paper, we extend this result… (More)

Nonlinearity of rotation symmetric Boolean functions is an important topic on cryptography algorithm. Let e ≥ 1 be any given integer. In this paper, we investigate the following question: Is the nonlinearity of the quartic rotation symmetric Boolean function generated by the monomial x 0 xex 2e x 3e equal to its weight? We introduce some new simple… (More)

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