2021/12/31 by Yansheng Wu, Wu, Yansheng, Chengju Li +3 · 1 citation
Computer Science · Engineering · Medicine · #Advanced Wireless Communication Techniques #Cancer Mechanisms and Therapy #Coding theory and cryptography #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.2112.15462
openalex publication_date 2021/12/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and defining sets. Second, we construct quaternary linear codes via simplicial complexes and determine the weight distributions of these codes. Third, the weight distributions of the binary subfield codes of these quaternary codes are also computed by employing the general characterization. Furthermore, we present two infinite families of optimal linear codes with respect to the Griesmer Bound, and a class of binary almost optimal codes with respect to the Sphere Packing Bound. We also need to emphasize that we obtain at least 9 new quaternary linear codes.