Modular Curves and Codes with Polynomial Construction Complexity

The authors construct and analyze linear $q$-ary codes that arise from modular Drinfeld, and the associated binary codes. All these codes have polynomial complexity of construction and “good” asymptotic parameters: $q4-ary codes for $q=p^{2m}\geq 49$ lie above the Varshamov–Gilbert bound on some segment, while binary codes lie above the Blokh–Zyablov bound everywhere.