Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Sabo, Eric, Can, Mahir Bilen, Marquis, David
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204840502