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Linear Codes From Perfect Nonlinear Functions Over Finite Fields
IEEE Transactions on Communications ( IF 5.690 ) Pub Date : 2019-11-14 , DOI: 10.1109/tcomm.2019.2953674
Yanan Wu; Nian Li; Xiangyong Zeng

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 $\mathbb {F}_{p^{m}}$ and $(m,s)$ -bent functions from $\mathbb {F}_{2^{m}}$ to $\mathbb {F}_{2^{s}}$ , 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.
更新日期:2020-01-17

 

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