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Updated: Jul 18, 2025

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Published on: June 8, 2018
On Optimal and Quantum Code Construction from Cyclic Codes over FqPQ with Applications
Shakir Ali1, Amal S Alali2, Pushpendra Sharma1
1Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India.
Abstract:
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.
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