Constructions of optimal locally recoverable codes via Dickson polynomials

被引：0
|
作者：
Jian Liu
Sihem Mesnager
Deng Tang
机构：
[1] Tianjin University,School of Cybersecurity, College of Intelligence and Computing
[2] State Key Laboratory of Cryptology,Department of Mathematics
[3] University of Paris VIII,School of Electronic Information and Electrical Engineering
[4] LAGA UMR 7539,undefined
[5] CNRS,undefined
[6] Sorbonne Paris Cité,undefined
[7] University of Paris XIII,undefined
[8] Telecom ParisTech,undefined
[9] Shanghai Jiao Tong University,undefined
来源：
Designs, Codes and Cryptography | 2020年 / 88卷
关键词：
Locally recoverable code; Dickson polynomial; Polynomial over a finite field; Linear code; Primary: 11C08; 12-00 Secondary: 94B05;
D O I：
暂无
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学科分类号：
摘要：
In 2014, Tamo and Barg have presented in a very remarkable paper a family of optimal linear locally recoverable codes (LRC codes) that attain the maximum possible distance (given code length, cardinality, and locality). The key ingredients for constructing such optimal linear LRC codes are the so-called r-good polynomials, where r is equal to the locality of the LRC code. In 2018, Liu et al. presented two general methods of designing r-good polynomials by using function composition, which led to three new constructions of r-good polynomials. Next, Micheli provided a Galois theoretical framework which allows to construct r-good polynomials. The well-known Dickson polynomials form an important class of polynomials which have been extensively investigated in recent years in different contexts. In this paper, we provide new methods of designing r-good polynomials based on Dickson polynomials. Such r-good polynomials provide new constructions of optimal LRC codes.
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页码：1759 / 1780
页数：21
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