Note on the dimension of Goppa codes

被引：0

作者：

Quan, Xiaoshan ^{[1
]}

Yue, Qin ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing 211100, Peoples R China

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2024年 / 35卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Goppa codes; Dimensions; Polynomials; TRUE DIMENSION;

D O I：

10.1007/s00200-022-00578-z

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Let Gamma(L, g) be a Goppa code over F-q, where L subset of F-qm is a support and g(x) is an element of F-qm [x] is a polynomial with s distinct roots in F-qm. In [Couvreur A, Otmani A, Tillich JP (2014) New identities relating wild Goppa codes. Finite Field Appl 29: 178-197.], Couvreur at al. gave the bound: dim(Fq) Gamma(L, g(e)) - dim(Fq) Gamma(L, g(e+1)) <= s, where e = q(m-1) + q(m-2) + ... + q. In this paper, we give the conditions such that dim(Fq )Gamma(L, g(e)) = dim(Fq) Gamma(L, g(e+1)).

引用

页码：683 / 690

页数：8

共 50 条

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