Problem
Research questions and friction points this paper is trying to address.
bivariate bicycle codes
logical dimensions
minimum distances
code symmetries
Spectral Theory of Semisimple Bivariate Bicycle Codes
🤖 AI Summary
本文通过代数方法和Frobenius轨道幂等式解决了二元自行车码的逻辑维度计算及最小距离下界估计问题，并构建了结构化的坐标置换子群。
📝 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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
bivariate bicycle codes
Frobenius-orbit idempotents
code symmetries
block-monomial subgroup
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