One- and Two-Point Codes over Kummer Extensions

Autor:	Alonso Sepúlveda Castellanos, Ariane M. Masuda, Luciane Quoos
Rok vydání:	2015
Předmět:	Pure mathematics Semigroup Mathematics::Number Theory 020206 networking & telecommunications 0102 computer and information sciences 02 engineering and technology Library and Information Sciences Lambda 01 natural sciences Electronic mail Computer Science Applications Mathematics - Algebraic Geometry Algebraic geometric Mathematics::Algebraic Geometry 010201 computation theory & mathematics 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Point (geometry) Separable polynomial Algebraic Geometry (math.AG) Information Systems Mathematics
DOI:	10.48550/arxiv.1510.06425
Popis:	We compute the Weierstrass semigroup at one totally ramified place for Kummer extensions defined by $y^m=f(x)^{\lambda}$ where $f(x)$ is a separable polynomial over $\mathbb{F}_q$. 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. Comment: Some corrections were made. Final version to appear in the IEEE Transactions on Information Theory
Databáze:	OpenAIRE
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