Binary Linear Codes With Few Weights From Two-to-One Functions
Journal article, Peer reviewed
Accepted version
Permanent lenke
https://hdl.handle.net/11250/2986825Utgivelsesdato
2021Metadata
Vis full innførselSamlinger
- Department of Informatics [1002]
- Registrations from Cristin [11365]
Originalversjon
IEEE Transactions on Information Theory. 2021, 67 (7), 4263-4275 10.1109/TIT.2021.3068743Sammendrag
In this paper, we apply two-to-one functions over b F 2n in two generic constructions of binary linear codes. We consider two-to-one functions in two forms: (1) generalized quadratic functions; and (2) (x 2t +x) e with gcd(t, n)=gcd(e, 2 n -1)=1. Based on the study of the Walsh transforms of those functions or their variants, we present many classes of linear codes with few nonzero weights, including one weight, three weights, four weights, and five weights. The weight distributions of the proposed codes with one weight and with three weights are determined. In addition, we discuss the minimum distance of the dual of the constructed codes and show that some of them achieve the sphere packing bound. Moreover, examples show that some codes in this paper have best-known parameters.