Binary Linear Codes With Few Weights From Two-to-One Functions

In this paper, we apply two-to-one functions over b F 2n in two generic constructions of binary linear codes. We consider forms: (1) generalized quadratic functions; and (2) (x 2t +x) xmlns:xlink="http://www.w3.org/1999/xlink">e with gcd(t, n)=gcd(e, 2 xmlns:xlink="http://www.w3.org/1999/xlink">n -1)=1. Based on the study Walsh transforms those or their variants, present many classes codes few nonzero weights, including one weight, three four five weights. The weight distributions proposed weights are determined. addition, discuss minimum distance dual constructed show that some them achieve sphere packing bound. Moreover, examples paper have best-known parameters.