Quantum Codes from Galois Hulls of Constacyclic Codes over a Finite Non-Chain Ring
Abstract
We study the algebraic structures of constacyclic codes over a new finite non-chain ring R and their l-Galois dual codes based on a new Gray map ϕ and determine the dimensions of the l-Galois hull of constacyclic codes over R. Furthermore, we propose a quantum construction X of the Galois inner product to construct quantum codes by combining the Calderbank–Shor–Steane (CSS) construction, Hermitian construction and construction X. As an application, by calculating the dimensions of the l-Galois hull of constacyclic codes over R, we obtain some new quantum maximum distance separable (QMDS) codes and new quantum error-correcting codes (QECCs) that are better than the best known ones.
Fields of Study & Subjects
Quantum Computing Algorithms and Architecture
Coding theory and cryptography
Polynomial and algebraic computation
Publication details
- Journal / source
- Entropy
- Publisher
- MDPI AG
- Volume
- 28
- Issue
- 4
- Pages
- 407–407
- Publication date
- 3 April 2026
- Language
- EN