scholarly journals Optimal (r, δ)-Locally Repairable Codes From Simplex Code and Cap Code

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 215414-215418
Author(s):  
Qiang Fu ◽  
Ruihu Li ◽  
Sen Yang
Keyword(s):  
Simplex Code ◽  
Locally Repairable Codes

Improved Bounds and Singleton-Optimal Constructions of Locally Repairable Codes With Minimum Distance 5 and 6

2021 ◽  
Vol 67 (1) ◽  
pp. 217-231
Author(s):  
Bin Chen ◽  
Weijun Fang ◽  
Shu-Tao Xia ◽  
Jie Hao ◽  
Fang-Wei Fu
Keyword(s):  
Minimum Distance ◽  
Locally Repairable Codes

On some punctured codes of ℤq-Simplex codes

2021 ◽  
pp. 2250012
Author(s):  
J. Prabu ◽  
J. Mahalakshmi ◽  
C. Durairajan ◽  
S. Santhakumar
Keyword(s):  
Prime Divisor ◽  
Weight Distribution ◽  
Linear Code ◽  
Prime Power ◽  
Punctured Codes ◽  
New Codes ◽  
Simplex Codes ◽  
Simplex Code ◽  
Partial Weight ◽  
Unit Formula

In this paper, we have constructed some new codes from [Formula: see text]-Simplex code called unit [Formula: see text]-Simplex code. In particular, we find the parameters of these codes and have proved that it is a [Formula: see text] [Formula: see text]-linear code, where [Formula: see text] and [Formula: see text] is a smallest prime divisor of [Formula: see text]. When rank [Formula: see text] and [Formula: see text] is a prime power, we have given the weight distribution of unit [Formula: see text]-Simplex code. For the rank [Formula: see text] we obtain the partial weight distribution of unit [Formula: see text]-Simplex code when [Formula: see text] is a prime power. Further, we derive the weight distribution of unit [Formula: see text]-Simplex code for the rank [Formula: see text] [Formula: see text].

scholarly journals Constructions of Optimal Cyclic $({r},{\delta })$ Locally Repairable Codes

2018 ◽  
Vol 64 (4) ◽  
pp. 2499-2511 ◽  
Author(s):  
Bin Chen ◽  
Shu-Tao Xia ◽  
Jie Hao ◽  
Fang-Wei Fu
Keyword(s):  
Locally Repairable Codes

scholarly journals Optimal Locally Repairable Codes Via Elliptic Curves

2019 ◽  
Vol 65 (1) ◽  
pp. 108-117 ◽  
Author(s):  
Xudong Li ◽  
Liming Ma ◽  
Chaoping Xing
Keyword(s):  
Elliptic Curves ◽  
Locally Repairable Codes
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