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Linear Codes From Perfect Nonlinear Functions Over Finite Fields | IEEE Journals & Magazine | IEEE Xplore

Linear Codes From Perfect Nonlinear Functions Over Finite Fields


Abstract:

In this paper, a class of p-ary 3-weight linear codes and a class of binary 2-weight linear codes are proposed respectively by virtue of the properties of the perfect non...Show More

Abstract:

In this paper, a class of p-ary 3-weight linear codes and a class of binary 2-weight linear codes are proposed respectively by virtue of the properties of the perfect nonlinear functions over Fp(m) and (m, s)-bent functions from F2(m) to F2(s), where p is an odd prime and m, s are positive integers. The weight distributions are completely determined by the sign of the Walsh transform of weakly regular bent functions and the size of the preimage of the employed (m, s)-bent functions at the zero point, respectively. As a special case, a class of optimal linear codes meeting Griesmer bound is obtained from our construction.
Published in: IEEE Transactions on Communications ( Volume: 68, Issue: 1, January 2020)
Page(s): 3 - 11
Date of Publication: 14 November 2019

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