Spectral Theory of Semisimple Bivariate Bicycle Codes

• URL: http://arxiv.org/abs/2608.27565v1
• Date: Thu, 27 Aug 2026 18:00:04 GMT
• Title: Spectral Theory of Semisimple Bivariate Bicycle Codes
• Abstract summary: A systematic theory of code symmetries is formulated to construct a structured block-monomial subgroup of coordinate permutations.<n>An appendix extends the analysis to BCH-based product constructions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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