scholarly journals Bounds and Constructions of Locally Repairable Codes: Parity-Check Matrix Approach

2020 ◽  
Vol 66 (12) ◽  
pp. 7465-7474 ◽  
Author(s):  
Jie Hao ◽  
Shu-Tao Xia ◽  
Kenneth W. Shum ◽  
Bin Chen ◽  
Fang-Wei Fu ◽  
...  
Keyword(s):  
Matrix Approach ◽  
Parity Check ◽  
Parity Check Matrix ◽  
Check Matrix ◽  
Locally Repairable Codes

BCK-codes Based on a Parity Check Matrix

2020 ◽  
Vol 174 (2) ◽  
pp. 137-165
Author(s):  
Nazanin Keshavarzian ◽  
Arsham Borumand Saeid ◽  
Abolfazl Tehranian
Keyword(s):  
Parity Check ◽  
Parity Check Matrix ◽  
Check Matrix

scholarly journals New Soft Set Based Class of Linear Algebraic Codes

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 510 ◽  
Author(s):  
Mumtaz Ali ◽  
Huma Khan ◽  
Le Son ◽  
Florentin Smarandache ◽  
W. Kandasamy
Keyword(s):  
Error Detection ◽  
Parity Check ◽  
Generator Matrix ◽  
Parity Check Matrix ◽  
Soft Sets ◽  
New Class ◽  
Error Detection And Correction ◽  
Check Matrix ◽  
Algebraic Codes ◽  
Canonical Generator

In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example.

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