Browsing by Author "Stepanov, Serguei A."
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Item Open Access Fibre products of superelliptic curves and codes therefrom(IEEE, 1997) Stepanov, Serguei A.; Özbudak, FerruhA method of constructing long geometric Goppa codes coming from fiber products of superelliptic curves is presented. A family of smooth projective curves with a lot of Fq-rational points are needed to produce a family of asymptotically good geometric Goppa codes. The genus in every such family is considerably less than the number of rational points, so the corresponding geometric Goppa codes have rather good parameters. Examples of such families are provided by modular curves, by Drinfeld modular curves, and by Artin-Schreier coverings of the projective line.Item Open Access Fibre products, character sums and geometric Goppa codes(CRC Press, 1998) Stepanov, Serguei A.; Stepanov, Serguei A.; Yıldırım, Cem YalçınThe purpose of this paper is to construct some new families of smooth projective curves over a finite field Fq with extremely many Fq-rational points. The genus in every such family is considerably less than the number of rational points, and these two facts allow to produce sufficiently long geometric Gappa codes with very good parameters.Item Open Access Preface(CRC Press, 1998) Stepanov, Serguei A.; Stepanov, Serguei A.; Yıldırım, Cem Yalçın