2024/04/29 by Ziling Heng, Mengjie Yang, Heng, Ziling +3 · 1 citation
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2404.18437
openalex publication_date 2024/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Linear codes are widely studied due to their applications in communication, cryptography, quantum codes, distributed storage and many other fields. In this paper, we use the trace and norm functions over finite fields to construct a family of linear codes. The weight distributions of the codes are determined in three cases via Gaussian sums. The codes are shown to be self-orthogonal divisible codes with only three, four or five nonzero weights in these cases. In particular, we prove that this family of linear codes has locality 2. Several optimal or almost optimal linear codes and locally recoverable codes are derived. In particular, an infinite family of distance-optimal binary linear codes with respect to the sphere-packing bound is obtained. The self-orthogonal codes derived in this paper can be used to construct lattices and have nice application in distributed storage.