One- and Two-Point Codes Over Kummer Extensions

We compute the Weierstrass semigroup at one totally ramified place for Kummer extensions defined by y m = f (x) λ , where f (x) is a separable polynomial over F q . In addition, we compute the Weierstrass semigroup at two certain totally ramified places. We then apply our results to construct one- a...

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Bibliographic Details
Published in:	IEEE transactions on information theory Vol. 62; no. 9; pp. 4867 - 4872
Main Authors:	Castellanos, Alonso S., Masuda, Ariane M., Quoos, Luciane
Format:	Journal Article
Language:	English
Published:	New York IEEE 01-09-2016 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algebra Algebraic geometric codes Codes Construction Electronic mail Geometry Group theory Indexes Information theory Kummer extension Linear codes Parameters Polynomials Urban areas Weierstrass semigroup Writing
Online Access:	Get full text
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Summary:	We compute the Weierstrass semigroup at one totally ramified place for Kummer extensions defined by y m = f (x) λ , where f (x) is a separable polynomial over 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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2016.2583437