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Spectral Theory of Semisimple Bivariate Bicycle Codes
Abstract
Extending the classical theory of two-dimensional cyclic codes, we develop an algebraic approach to bivariate bicycle codes. Using Frobenius-orbit idempotents, formulas for logical dimensions are derived and lower bounds on minimum distances are established. A systematic theory of code symmetries is formulated to construct a structured block-monomial subgroup of coordinate permutations. Several explicit examples show how to generate these codes from first principles without relying on numerical searches. An appendix extends the analysis to BCH-based product constructions.
Related
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- Quantum bivariate bicycle codes with weight-8 checks surpassing the BB benchmark
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BibTeX
@misc{sabo2026spectral,
title = {{Spectral Theory of Semisimple Bivariate Bicycle Codes}},
author = {Eric Sabo and Mahir Bilen Can and David Marquis},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.27565},
eprint = {2608.27565},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.27565},
}
RIS
TY - UNPB
TI - Spectral Theory of Semisimple Bivariate Bicycle Codes
AU - Eric Sabo
AU - Mahir Bilen Can
AU - David Marquis
PY - 2026
DA - 2026/08/27
PB - arXiv
DO - 10.48550/arxiv.2608.27565
UR - https://arxiv.org/abs/2608.27565
AB - Extending the classical theory of two-dimensional cyclic codes, we develop an algebraic approach to bivariate bicycle codes. Using Frobenius-orbit idempotents, formulas for logical dimensions are derived and lower bounds on minimum distances are established. A systematic theory of code symmetries is formulated to construct a structured block-monomial subgroup of coordinate permutations. Several explicit examples show how to generate these codes from first principles without relying on numerical searches. An appendix extends the analysis to BCH-based product constructions.
ER -