Aliabadi, Zohreh and Kalaycı, Tekgül and Zadehdabbagh, Mohammad (2026) Asymptotic performance of double circulant and four circulant codes with small hull dimension. Cryptography and Communications . ISSN 1936-2447 (Print) 1936-2455 (Online) Published Online First https://dx.doi.org/10.1007/s12095-025-00861-z
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Official URL: https://dx.doi.org/10.1007/s12095-025-00861-z
Abstract
We present enumeration formulas for double circulant (DC) codes of length and four circulant (FC) codes of length over the finite field, with prescribed Euclidean hull dimension, assuming. These formulas significantly generalize previous results that were limited to special cases. In particular, we resolve an open problem posed by Zhu and Shi (J. Appl. Math. Comput. 68:1227–1244, 2022) concerning the case of reciprocal pair factors in the factorization of for the enumeration of self-dual and linear complementary dual (LCD) FC codes. Additionally, we correct an enumeration formula used in Zhu and Shi (Bull. Aust. Math. Soc. 98(1):159–166, 2018), leading to an improved bound on the relative distance for LCD FC codes.
| Item Type: | Article |
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| Additional Information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Uncontrolled Keywords: | Artin’s primitive root conjecture; Double circulant code; Four circulant code; Linear complementary dual code; Quasi-cyclic code; The hull of a code |
| Divisions: | Faculty of Engineering and Natural Sciences |
| Depositing User: | Zohreh Aliabadi |
| Date Deposited: | 27 Mar 2026 12:46 |
| Last Modified: | 27 Mar 2026 12:46 |
| URI: | https://research.sabanciuniv.edu/id/eprint/53654 |
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