Cyclic codes over non-chain ring R(α1, α2,…, αs) and their applications to quantum and DNA codes
| dc.authorid | 0000-0003-0032-3400 | en_US |
| dc.contributor.author | Ali, Shakir | |
| dc.contributor.author | Alali, Amal S. | |
| dc.contributor.author | Wong, Kok Bin | |
| dc.contributor.author | Öztaş, Elif Segah | |
| dc.contributor.author | Sharma, Pushpendra | |
| dc.date.accessioned | 2024-07-11T07:31:02Z | |
| dc.date.available | 2024-07-11T07:31:02Z | |
| dc.date.issued | 2024 | en_US |
| dc.department | KMÜ, Kamil Özdağ Fen Fakültesi, Matematik Bölümü | en_US |
| dc.description.abstract | Let s ≥ 1 be a fixed integer. In this paper, we focus on generating cyclic codes over the ring R(α1, α2, …, αs), where αi ∈ Fq \{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 Fq reversibility. The aim to introduce the Fq reversibility is to describe IUPAC nucleotide codes, and consequently, 5 IUPAC DNA bases are considered instead of 4 DNA bases (A, T, G, C). © 2024 the Author(s), licensee AIMS Press. | en_US |
| dc.identifier.citation | Ali, S., Alali, A.S., Wong, K.B., Öztaş, E.S., Sharma, P. (2024). Cyclic codes over non-chain ring and their applications to quantum and DNA codes.AIMS Mathematics, 9 (3). https://doi.org/10.3934/math.2024358 | en_US |
| dc.identifier.doi | 10.3934/math.2024358 | |
| dc.identifier.issn | 2473-6988 | |
| dc.identifier.issue | 3 | en_US |
| dc.identifier.scopus | 2-s2.0-85187886211 | |
| dc.identifier.scopusquality | Q1 | |
| dc.identifier.uri | https://doi.org/10.3934/math.2024358 | |
| dc.identifier.uri | https://hdl.handle.net/11492/8463 | |
| dc.identifier.volume | 9 | en_US |
| dc.identifier.wos | WOS:001207685200007 | |
| dc.identifier.wosquality | N/A | |
| dc.indekslendigikaynak | Web of Sceince | |
| dc.indekslendigikaynak | Scopus | |
| dc.institutionauthor | Öztaş, Elif Segah | |
| dc.language.iso | en | |
| dc.publisher | American Institute of Mathematical Sciences | en_US |
| dc.relation.journal | AIMS Mathematics | en_US |
| dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Cyclic Code | en_US |
| dc.subject | DNA Code | en_US |
| dc.subject | DNA Reversibility | en_US |
| dc.subject | Gray Map | en_US |
| dc.subject | Non-Chain Ring | en_US |
| dc.subject | Quantum Code | en_US |
| dc.title | Cyclic codes over non-chain ring R(α1, α2,…, αs) and their applications to quantum and DNA codes | en_US |
| dc.type | Article |
