Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3545
Abstract
The Euclidean hull of a linear code C is defined as C ∩ C⊥ , where C⊥ denotes the dual of C underthe Euclidean inner product. A linear code with the trivial hull is called a linear complementary dual (LCD) code. Apair (C,D) of linear codes of length n over the finite field Fq is called a linear complementary pair (LCP) of codes ifC ⊕ D = Fnq. More generally, a pair (C,D) of linear codes of the same length over Fq is called a linear ℓ -intersectionpair of codes if C ∩D has dimension ℓ as a vector space over Fq . In this paper, we give characterizations of LCD, LCPof cyclic codes and one-dimensional hull cyclic codes of length qm − 1, m ≥ 1, over Fq in terms of their basic dual zerosets and their trace representations. We also formulate the hull dimension of a cyclic code of arbitrary length over Fqwith respect to its basic dual zero set. Moreover, we provide a general formula for the dimension ℓ of the intersection oftwo cyclic codes of arbitrary length over Fq based on their basic dual zero sets.
Keywords
Cyclic codes, hull of linear codes, linear complementary dual codes, linear complementary pair of codes, trace representation, basic dual zero set
First Page
861
Last Page
873
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
ALIABADI, ZOHREH and KALAYCI, TEKGÜL
(2024)
"A note on the hull and linear complementary pair of cyclic codes,"
Turkish Journal of Mathematics: Vol. 48:
No.
5, Article 4.
https://doi.org/10.55730/1300-0098.3545
Available at:
https://journals.tubitak.gov.tr/math/vol48/iss5/4
