On Optimal and Quantum Code Construction from Cyclic Codes over
<inline-formula><math display="inline"><semantics><mrow><mi mathvariant="fraktur">F</mi></mrow></semantics></math></inline-formula><sub>q</sub><i>PQ</i> with Applications
Shakir Ali,
Amal S. Alali,
Pushpendra Sharma,
Kok Bin Wong,
Elif Segah Öztas,
Mohammad Jeelani
Affiliations
Shakir Ali
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
Amal S. Alali
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Pushpendra Sharma
Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
Kok Bin Wong
Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia
Elif Segah Öztas
Department of Mathematics, Kamil Ozdag Science Faculty, Karamanoglu Mehmetbey University, Karaman 70100, Turkey
Mohammad Jeelani
Department of Computer Application, Faculty of Science, Integral University, Lucknow 226026, India
The key objective of this paper is to study the cyclic codes over mixed alphabets on the structure of FqPQ, where P=Fq[v]⟨v3−α22v⟩ and Q=Fq[u,v]⟨u2−α12,v3−α22v⟩ are nonchain finite rings and αi is in Fq/{0} for i∈{1,2}, where q=pm with m≥1 is a positive integer and p is an odd prime. Moreover, with the applications, we obtain better and new quantum error-correcting (QEC) codes. For another application over the ring P, we obtain several optimal codes with the help of the Gray image of cyclic codes.
