1. Combinatorial Constructions of Optimal Quaternary Additive Codes
- Author
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Guan, Chaofeng, Lv, Jingjie, Luo, Gaojun, and Ma, Zhi
- Subjects
Computer Science - Information Theory - Abstract
This paper aims to construct optimal quaternary additive codes with non-integer dimensions. Firstly, we propose combinatorial constructions of quaternary additive constant-weight codes, alongside additive anticode construction. Subsequently, we propose generalized Construction X, which facilitates the construction of non-integer dimensional optimal additive codes from linear codes. Then, we construct ten classes of optimal quaternary non-integer dimensional additive codes through these two methods. As an application, we also determine the optimal additive $[n,3.5,n-t]_4$ codes for all $t$ with variable $n$, except for $t=6,7,12$., Comment: This work was mainly completed in the summer of 2023, and here we add some new developments. Everyone is welcome to discuss issues related to additional code with the first author
- Published
- 2024