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We study a broad class of qudit stabilizer codes, termed ZN bivariate-bicycle (BB) codes, arising either as two-dimensional realizations of modulated gauge theories or as ZN generalizations of binary BB codes. Our central finding, derived from the polynomial representation, is that the essential topological properties of these ZN codes can be determined by the properties of their Zₚ counterparts, where p are the prime factors of N, even when N contains prime powers (N = ᵢ pᵢ^kᵢ). This result yields a significant simplification by leveraging the well-studied framework of codes with prime qudit dimensions. In particular, this insight directly enables the generalization of the algebraic-geometric methods (e. g. , the Bernstein-Khovanskii-Kushnirenko theorem) to determine anyon fusion rules in the general qudit situation. Moreover, we elucidate the symmetry-enriched topological (SET) order underlying the quasifractonic behavior in qudit BB codes (including the Delfino-Chamon-You model), resolving the associated anyon mobility puzzle. We also develop an efficient computational algebraic method, based on Gröbner bases over the ring of integers, to determine both the topological order and its SET properties.
He et al. (Thu,) studied this question.