具有优良渐近参数的代数几何码(英文)

ALGEBRAIC GEOMETRY CODES WITH GOOD ASYMPTOTIC PARAMETERS

本文讨论了一类具有好的渐近参数的代数几何码.通过对除子类数、高次有理除子数以及代数几何码的参数分析,得到一类码其渐近界优于Gilbert-Varshamov界和Xing界.在这两个界的交点处,渐近界有所改进.

In this paper, we discuss a class of algebraic geometry codes （A-G codes） with good asymptotic parameters. Based on some analyses on a relation amony divisor class number, number of rational divisors of high degrees, and parameters of A-G codes, we obtain an asymptotic bound of a class, which is better than both the Gilbert-Varshamov and the Xing bounds. Our result shows that these two bounds can be improved significantly around the two points where they intersect.