Work

One- and Two-Point Codes Over Kummer Extensions

Year: 2016

Type: article

Abstract: We compute the Weierstrass semigroup at one totally ramified place for Kummer extensions defined by ym= f (x)λ, where f (x) is a separable polynomial over Fq. In addition, we compute the Weierstrass semigroup at two certain totally ramified places. We then apply our results to construct one- and two-point algebraic geometric codes with good parameters.

Source: IEEE Transactions on Information Theory

DOI: 10.1109/tit.2016.2583437

Authors: Alonso S. Castellanos, Ariane M. Masuda, Luciane Quoos

Institutions: Universidade Federal de Uberlândia, City University of New York, Universidade Federal do Rio de Janeiro

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: City University of New York, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Fundação de Amparo à Pesquisa do Estado de Minas Gerais

Awards: G4661525740, SEMIGRUPO DE WEIERSSTRASS E CÓDIGOS SOBRE UMA FAMÍLIA DE CURVAS CASTELO., G757987663