On the stopping distance of LDPC codes based on symplectic space over finite fields

2021 ◽  
Vol 391 ◽  
pp. 125625
Author(s):  
You Gao ◽  
Yun-Fei Yao ◽  
He Ma
Keyword(s):  
Finite Fields ◽  
Ldpc Codes ◽  
Symplectic Space ◽  
Stopping Distance

Quasi-Cyclic LDPC Codes on Cyclic Subgroups of Finite Fields

2011 ◽  
Vol 59 (9) ◽  
pp. 2330-2336 ◽  
Author(s):  
Li Zhang ◽  
Shu Lin ◽  
Khaled Abdel-Ghaffar ◽  
Zhi Ding ◽  
Bo Zhou
Keyword(s):  
Finite Fields ◽  
Ldpc Codes ◽  
Cyclic Subgroups

Constructions of compressed sensing matrices based on the subspaces of symplectic space over finite fields

2015 ◽  
Vol 15 (02) ◽  
pp. 1650025 ◽  
Author(s):  
You Gao ◽  
Xiaojuan Zhang
Keyword(s):  
Compressed Sensing ◽  
Finite Fields ◽  
Symplectic Geometry ◽  
Symplectic Space ◽  
The Matrix ◽  
Compressed Sensing Matrices ◽  
Sensing Matrices

The paper provides two constructions of compressed sensing matrices using the subspaces of symplectic space and singular symplectic space over finite fields. Then we compare the matrices constructed in this paper with the matrix constructed by DeVore, and compare the two matrices based on symplectic geometry and singular symplectic geometry over finite fields.

Constructions of (r,t)-LRC Based on Totally Isotropic Subspaces in Symplectic Space Over Finite Fields

2020 ◽  
Vol 31 (03) ◽  
pp. 327-339
Author(s):  
Gang Wang ◽  
Min-Yao Niu ◽  
Fang-Wei Fu
Keyword(s):  
Finite Fields ◽  
Linear Codes ◽  
Distributed Storage ◽  
Symplectic Space ◽  
Information Rate ◽  
Local Repair ◽  
Distributed Storage Systems ◽  
Isotropic Subspaces ◽  
Locally Repairable Codes ◽  
Totally Isotropic Subspaces

Linear code with locality [Formula: see text] and availability [Formula: see text] is that the value at each coordinate [Formula: see text] can be recovered from [Formula: see text] disjoint repairable sets each containing at most [Formula: see text] other coordinates. This property is particularly useful for codes in distributed storage systems because it permits local repair of failed nodes and parallel access of hot data. In this paper, two constructions of [Formula: see text]-locally repairable linear codes based on totally isotropic subspaces in symplectic space [Formula: see text] over finite fields [Formula: see text] are presented. Meanwhile, comparisons are made among the [Formula: see text]-locally repairable codes we construct, the direct product code in Refs. [8], [11] and the codes in Ref. [9] about the information rate [Formula: see text] and relative distance [Formula: see text].

On the stopping distance of finite geometry ldpc codes

2006 ◽  
Vol 10 (5) ◽  
pp. 381-383 ◽  
Author(s):  
Shu-Tao Xia ◽  
Fang-Wei Fu
Keyword(s):  
Ldpc Codes ◽  
Finite Geometry ◽  
Stopping Distance
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