Combinatorial Constructions of Optimal Quaternary Additive Codes
<|reference_start|>Combinatorial Constructions of Optimal Quaternary Additive Codes: 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 $t=6,7,12$.<|reference_end|>
@article{guan2024combinatorial,
    title={Combinatorial Constructions of Optimal Quaternary Additive Codes},
    author={Chaofeng Guan, Jingjie Lv, Gaojun Luo, Zhi Ma},
    journal={arXiv preprint arXiv:2407.04193},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.04193},
    primaryClass={cs.IT math.IT}
}