On the complete weight enumerators of some linear codes with a few weights
This work provides incremental improvements in coding theory, benefiting applications like authentication codes and secret sharing.
The paper tackled the problem of determining complete weight enumerators for certain classes of linear codes with few weights, and derived the corresponding Hamming weight distributions using sums involving the Legendre symbol.
Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of linear codes are important research topics. In this paper, we consider some classes of linear codes with a few weights and determine the complete weight enumerators from which the corresponding Hamming weight distributions are derived with help of some sums involving Legendre symbol.