Ο β Constacyclic codes over a Frobenius ring and their application to find novel quantum codes
Abstract
In this work, we use the Hermitian technique to find novel Quantum error correcting codes (π¬Eππβs) by Constacyclic codes (CCcβs) over the ring β = β±p2 [π, π]/(π3 β Ο2 π, π3 β Ο2 π), where p is a non-even prime power and β±*p 2 = β©Οβͺ. Firstly, we express the ring in terms of βpairwise orthogonal Idempotentβ elements & analyze βlinear codes.β We investigate ring structure and establish a one-one, onto and distance preserving Gray map, β
βΆ βπββ±5π p2. We provide the units of β, to analyze CCcβs & their generators. We also give a condition for this code to contain its Hermitian dual over β. At last, we derive and tabulate some novel and efficient π¬Eππβs.
Fields of Study & Subjects
Coding theory and cryptography
Quantum Computing Algorithms and Architecture
Cryptography and Residue Arithmetic
Publication details
- Journal / source
- Journal of Discrete Mathematical Sciences and Cryptography
- Volume
- 29
- Issue
- 1
- Pages
- 229β241
- Publication date
- 1 January 2026