One-point codes using places of higher degree

Author

Matthews, Gretchen L. ; Michel, Todd W.

Author_Institution

Dept. of Math. Sci., Clemson Univ., SC, USA

Volume

51

Issue

4

fYear

2005

fDate

4/1/2005 12:00:00 AM

Firstpage

1590

Lastpage

1593

Abstract

In IEEE Transactions on Information Theory , vol. 48, no. 2, pp. 535-537, Feb. 2002, Xing and Chen show that there exist algebraic-geometry (AG) codes from the Hermitian function field over F_q² constructed using F_q²-rational divisors which are improvements over the much-studied one-point Hermitian codes. In this correspondence, we construct such codes by using a place P of degree r > 1. This motivates a study of gap numbers and pole numbers at places of higher degree. In fact, the code parameters are estimated using the Weierstrass gap set of the place P and relating it to the gap set of the r-tuple of places of degree one lying over P in a constant field extension of degree r.

Keywords

Hermitian matrices; IEEE standards; algebraic geometric codes; F_q²-rational divisor; Hermitian function field; IEEE transaction; Weierstrass gap set; algebraic-geometry code; code parameter; constant field extension; gap-pole number; information theory; one-point code; Codes; Parameter estimation; Algebraic-geometry (AG) code; Hermitian function field; Weierstrass gap set; degree of a place; one-point code;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2005.844058

Filename

1412053