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Spectral Theory of Semisimple Bivariate Bicycle Codes

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Eric Sabo, Mahir Bilen Can, David Marquis (Aug 31 2026).

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.

Arxiv: https://arxiv.org/abs/2608.27565

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