Title :
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
fDate :
4/1/2005 12:00:00 AM
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 Fq2 constructed using Fq2-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; Fq2-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;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2005.844058
