On MDS geometric Fq-linear Fqt-codes

被引：0
作者：
Ren, Yuan [1 ]
Han, Dongchun [2 ]
机构：
[1] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Peoples R China
[2] Southwest Jiaotong Univ, Dept Math, Chengdu 610000, Peoples R China
来源：
DISCRETE MATHEMATICS | 2023年 / 346卷 / 01期
基金：
中国国家自然科学基金;
关键词：
MDS codes; F-q-linear F-qt-codes; Algebraic geometry codes; Elliptic curves; MAIN CONJECTURE;
D O I：
10.1016/j.disc.2022.113125
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let F-q be a finite field and t be a positive integer. We first generalize the construction of algebraic-geometric codes to the setting of F-q-linear Fqt-codes. Then we show that such codes arising from the projective line yield MDS (resp. self-dual MDS) F-q-linear F-qt-codes (resp. when q is a power of 2). We also derive a tight upper bound for the maximal length of primitive MDS elliptic F-q-linear F-qt-codes with F-q-dimension k divided by t and satisfies 3 <= k/t <= q+1-2 root q/20 . (C) 2022 Elsevier B.V. All rights reserved.
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页数：9
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