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.

Quantum Physics (quant-ph); Information Theory (cs.IT)

arXiv:2608.27565 [quant-ph]

(or arXiv:2608.27565v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.27565 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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