Ali, Shakir and Alali, Amal S. and Wong, Kok Bin and Oztas, Elif Segah and Sharma, Pushpendra (2024) Cyclic codes over non-chain ring R(α1, α2, ... , αs) and their applications to quantum and DNA codes. AIMS Mathematics, 9 (3). pp. 7396-7413. ISSN 2473-6988, DOI https://doi.org/10.3934/math.2024358.
Full text not available from this repository.Abstract
Let s >= 1 be a fixed integer. In this paper, we focus on generating cyclic codes over the ring R(alpha(1), alpha(2), ... , alpha(s)), where alpha(i) is an element of F-q\textbackslash{0}, 1 <= i <= s, by using the Gray map that is defined by the idempotents. Moreover, we describe the process to generate an idempotent by using the formula (2.1). As applications, we obtain both optimal and new quantum codes. Additionally, we solve the DNA reversibility problem by introducing F-q reversibility. The aim to introduce the F-q reversibility is to describe IUPAC nucleotide codes, and consequently, 5 IUPAC DNA bases are considered instead of 4 DNA bases (A, T, G, C).
| Item Type: | Article |
|---|---|
| Funders: | Princess Nourah bint Abdulrahman University (PNU) , Riyadh, Saudi Arabia under Researchers Supporting Project (PNURSP2024R231), Institute of Mathematical Sciences (IMS) , University of Malaya (UM) , Malaysia |
| Uncontrolled Keywords: | cyclic code; quantum code; Gray map; non-chain ring; DNA code; DNA reversibility |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Institute of Mathematical Sciences |
| Depositing User: | Ms. Juhaida Abd Rahim |
| Date Deposited: | 13 Nov 2024 02:43 |
| Last Modified: | 13 Nov 2024 02:43 |
| URI: | http://eprints.um.edu.my/id/eprint/45838 |
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