Quantum Constacyclic BCH Codes over Qudits: A Spectral-Domain Approach
| Autor: | Patel, Shikha, Garani, Shayan Srinivasa |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We characterize constacyclic codes in the spectral domain using the finite field Fourier transform (FFFT) and propose a reduced complexity method for the spectral-domain decoder. Further, we also consider repeated-root constacyclic codes and characterize them in terms of symmetric and asymmetric $q$-cyclotomic cosets. Using zero sets of classical self-orthogonal and dual-containing codes, we derive quantum error correcting codes (QECCs) for both constacyclic Bose-Chaudhuri-Hocquenghem (BCH) codes and repeated-root constacyclic codes. We provide some examples of QECCs derived from repeated-root constacyclic codes and show that constacyclic BCH codes are more efficient than repeated-root constacyclic codes. Finally, quantum encoders and decoders are also proposed in the transform domain for Calderbank-Shor-Steane CSS-based quantum codes. Since constacyclic codes are a generalization of cyclic codes with better minimum distance than cyclic codes with the same code parameters, the proposed results are practically useful. Comment: 40 pages, 2 figures |
| Databáze: | arXiv |
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