Year: 2024
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Patel, Shikha, Garani, Shayan Srinivasa
Institution: Texas Instruments (Norway)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Indian Institute of Science
OpenAlex ID: W6891939996
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