Asymptotic performance of double and four circulant codes with small hull dimension
Abstract
We study the asymptotic behavior of double and four circulant codes, which are quasi-cyclic codes of index two and four respectively. Exact enumeration results are derived for these families of codes with the prescribed hull dimension. These formulas, in turn, are the most used tools to prove the good behavior of double circulant and four circulant codes asymptotically. Computational results on the code families in consideration are provided as well.
Keywords
Cite
@article{arxiv.2401.07017,
title = {Asymptotic performance of double and four circulant codes with small hull dimension},
author = {Zohreh Aliabadi and Tekgül Kalaycı},
journal= {arXiv preprint arXiv:2401.07017},
year = {2025}
}
Comments
We have added a new co-author and decided to withdraw all versions of this submission. Some of our earlier generalizations may be misleading due to differing approaches in the literature. To prevent confusion and ensure accurate interpretation of prior results, we are withdrawing the paper entirely