Self-orthogonal codes from plateaued functions

2024/11/07 by Peng Wang, Ziling Heng, Wang, Peng +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · #DNA and Biological Computing #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.2411.04447

openalex publication_date 2024/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Self-orthogonal codes are of interest as they have important applications in quantum codes, lattices and many areas. In this paper, based on the weakly regular plateaued functions or plateaued Boolean functions, we construct a family of linear codes with four nonzero weights. This family of linear codes is proved to be not only self-orthogonal but also optimally or almost optimally extendable. Besides, we derive binary and ternary linearly complementary dual codes (LCD codes for short) with new parameters from this family of codes. Some families of self-dual codes are also obtained as byproducts.

Cited by

• Constructions of binary self-orthogonal singly-even minimal linear codes violating the Aschikhmin-Barg condition with few weights

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