2017/01/09 by Shudi Yang, Yang, Shudi, Xiangli Kong +3
Computer Science · Engineering · #11T71 #94B15 #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.1701.02075
openalex publication_date 2017/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, linear codes constructed from defining sets have been studied extensively. They may have nice parameters if the defining set is chosen properly. Let m >2 be a positive integer. For an odd prime p , let r=pm and Tr be the absolute trace function from \mathbbFr onto \mathbbFp. In this paper, we give a construction of linear codes by defining the code CD=\(Tr(ax))x∈ D: a ∈ \mathbbFr \, where D =\x∈ \mathbbFr : Tr(x)=1, Tr(x2)=0 \. Its complete weight enumerator and weight enumerator are determined explicitly by employing cyclotomic numbers and Gauss sums. In addition, we obtain several optimal linear codes with a few weights. They have higher rate compared with other codes, which enables them to have essential applications in areas such as association schemes and secret sharing schemes.