Shortened linear codes from APN and PN functions

07/12/2020

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by   Can Xiang, et al.

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Linear codes generated by component functions of perfect nonlinear (PN for short) and almost perfect nonlinear (APN for short) functions and first-order Reed-Muller codes have been an object of intensive study by many coding theorists. In this paper, we investigate some binary shortened code of two families of linear codes from APN functions and some p-ary shortened codes from PN functions. The weight distributions of these shortened codes and the parameters of their duals are determined. The parameters of these binary codes and p-ary codes are flexible. Many of the codes presented in this paper are optimal or almost optimal in the sense that they meet some bound on linear codes. These results show high potential for shortening to be used in designing good codes.