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.

引用

页数：9

共 23 条

[11] Huffman W. Cary, 2010, International Journal of Information and Coding Theory, V1, P249, DOI 10.1504/IJICOT.2010.032543
[12] ON THE THEORY OF Fq-LINEAR Fqt-CODES
Huffman, W. Cary
[J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2013, 7 (03) : 349 - 378
[13] SELF-DUAL Fq-LINEAR Fqt-CODES WITH AN AUTOMORPHISM OF PRIME ORDER
Huffman, W. Cary
[J]. ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2013, 7 (01) : 57 - 90
[14] New MDS Self-Dual Codes From Generalized Reed-Solomon Codes
Jin, Lingfei
Xing, Chaoping
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2017, 63 (03) : 1434 - 1438
[15] Application of Classical Hermitian Self-Orthogonal MDS Codes to Quantum MDS Codes
Jin, Lingfei
Ling, San
Luo, Jinquan
Xing, Chaoping
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2010, 56 (09) : 4735 - 4740
[16] Katsman G. L., 1987, Problems of Information Transmission, V23, P262
[17] Kneser M., 1955, MATH Z, V61, P429, DOI [10.1007/BF01181357, DOI 10.1007/BF01181357]
[18] Lang S., 2002, Graduate Texts in Mathematics, V211
[19] ON THE MAIN CONJECTURE ON GEOMETRIC MDS CODES
MUNUERA, C
[J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 1992, 38 (05) : 1573 - 1577
[20] Shi MJ, 2015, J SYST SCI COMPLEX, V28, P679, DOI 10.1007/s11424-015-3265-3

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