Enumeration of linear codes with different hulls
<|reference_start|>Enumeration of linear codes with different hulls: The hull of a linear code $C$ is the intersection of $C$ with its dual code. We present and analyze the number of linear $q$-ary codes of the same length and dimension but with different dimensions for their hulls. We prove that for given dimension $k$ and length $n\ge 2k$ the number of all $[n,k]_q$ linear codes with hull dimension $l$ decreases as $l$ increases. We also present classification results for binary and ternary linear codes with trivial hulls (LCD and self-orthogonal) for some values of the length $n$ and dimension $k$, comparing the obtained numbers with the number of all linear codes for the given $n$ and $k$.<|reference_end|>
@article{bouyuklieva2024enumeration,
    title={Enumeration of linear codes with different hulls},
    author={Stefka Bouyuklieva and Iliya Bouyukliev},
    journal={arXiv preprint arXiv:2402.01255},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.01255},
    primaryClass={cs.IT cs.DM math.IT}
}