Aliabadi, Zohreh and Kalaycı, Tekgül (2024) A note on the hull and linear complementary pair of cyclic codes. Turkish Journal of Mathematics, 48 (5). pp. 861873. ISSN 13000098 (Print) 13036149 (Online)
This is the latest version of this item.
Official URL: https://dx.doi.org/10.55730/13000098.3545
Abstract
The Euclidean hull of a linear code C is defined as C ∩ C⊥, where C⊥ denotes the dual of C under the Euclidean inner product. A linear code with the trivial hull is called a linear complementary dual (LCD) code. A pair (C, D) of linear codes of length n over the finite field \BbbFq is called a linear complementary pair (LCP) of codes if C ⊕ D = \BbbFnq. More generally, a pair (C, D) of linear codes of the same length over \BbbFq is called a linear ℓintersection pair of codes if C ∩ D has dimension ℓ as a vector space over \BbbFq. In this paper, we give characterizations of LCD, LCP of cyclic codes and onedimensional hull cyclic codes of length qm − 1, m ≥ 1, over \BbbFq in terms of their basic dual zero sets and their trace representations. We also formulate the hull dimension of a cyclic code of arbitrary length over \BbbFq with respect to its basic dual zero set. Moreover, we provide a general formula for the dimension ℓ of the intersection of two cyclic codes of arbitrary length over \BbbFq based on their basic dual zero sets.
Item Type:  Article 

Uncontrolled Keywords:  basic dual zero set; Cyclic codes; hull of linear codes; linear complementary dual codes; linear complementary pair of codes; trace representation 
Divisions:  Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences 
Depositing User:  Tekgül Kalaycı 
Date Deposited:  28 Sep 2024 21:48 
Last Modified:  28 Sep 2024 21:48 
URI:  https://research.sabanciuniv.edu/id/eprint/50207 
Available Versions of this Item

A note on the hull and linear complementary pair of cyclic codes. (deposited 10 Jun 2024 15:09)
 A note on the hull and linear complementary pair of cyclic codes. (deposited 28 Sep 2024 21:48) [Currently Displayed]