On the Complete Weight Distribution of Subfield Subcodes of Algebraic-Geometric Codes

被引：3

作者：

Chan, Chin Hei ^{[1
]}

Xiong, Maosheng ^{[1
]}

机构：

[1] Hong Kong Univ Sci & Technol, Hong Kong, Peoples R China

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2019年 / 65卷 / 11期

关键词：

Complete weight distribution; subfield subcode; algebraic-geometric code; generalized Krawtchouk polynomial; TRUE DIMENSION; KRAWTCHOUK POLYNOMIALS; ENUMERATORS;

D O I：

10.1109/TIT.2019.2922630

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we first study deviations of the complete weight distribution of a linear code from that of a random code. Then, we consider a large family of subfield subcodes of algebraic-geometric codes over prime fields which include BCH codes and Goppa codes and prove that the complete weight distribution is close to that of a random code if the code length is large compared with the genus of the curve and the degree of the divisor defining the code.

引用

页码：7079 / 7086

页数：8

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