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Modular curves and codes with polynomial complexity of construction. (English. Russian original) Zbl 0555.94008
Probl. Inf. Transm. 20, 35-42 (1984); translation from Probl. Peredachi Inf. 20, No. 1, 47-55 (1984).
The authors construct and analyze linear $$q$$-ary codes that arise from modular Drinfel’d curves, and the associated binary codes. All these codes have polynomial complexity of construction and “good” asymptotic parameters: $$q$$-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.

##### MSC:
 94B05 Linear codes (general theory) 14H45 Special algebraic curves and curves of low genus