Hull's Parameters of Projective Reed-Muller Code
<|reference_start|>Hull's Parameters of Projective Reed-Muller Code: Projective Reed-Muller codes(PRM codes) are constructed from the family of projective hypersurfaces of a fixed degree over a finite field $\F_q$. In this paper, we completely determine the minimal distance of the hull of any Projective Reed-Muller codes. Motivated by Nathan Kaplan and Jon-Lark Kim \cite{kaplankim},we extend their results and calculate the hulls' dimension of Projective Reed-Muller Codes in a larger range. We also analyse two special classes of PRM codes apart from self-dual,self-orthgonal and LCD cases, which Kaplan and Kim \cite[section 3]{kaplankim} didn't consider.<|reference_end|>
@article{song2024hull's,
    title={Hull's Parameters of Projective Reed-Muller Code},
    author={Yufeng Song and Jinquan Luo},
    journal={arXiv preprint arXiv:2410.07217},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.07217},
    primaryClass={cs.IT math.IT}
}