scholarly journals Construction of matrix product codes where defining matrix is generator matrix of some BCH code or RS code, using SageMath functions

2021 ◽  
Keyword(s):  
Bch Code ◽  
Matrix Product ◽  
Generator Matrix ◽  
Product Codes ◽  
Rs Code

scholarly journals Matrix-Product Codes over Commutative Rings and Constructions Arising from σ , δ -Codes

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Mhammed Boulagouaz ◽  
Abdulaziz Deajim
Keyword(s):  
Lower Bound ◽  
Commutative Ring ◽  
Finite Fields ◽  
Hamming Distance ◽  
Commutative Rings ◽  
Matrix Product ◽  
Sufficient Condition ◽  
Generator Matrix ◽  
Product Codes ◽  
Product Code

A well-known lower bound (over finite fields and some special finite commutative rings) on the Hamming distance of a matrix-product code (MPC) is shown to remain valid over any commutative ring R . A sufficient condition is given, as well, for such a bound to be sharp. It is also shown that an MPC is free when its input codes are all free, in which case a generator matrix is given. If R is finite, a sufficient condition is provided for the dual of an MPC to be an MPC, a generator matrix for such a dual is given, and characterizations of LCD, self-dual, and self-orthogonal MPCs are presented. Finally, the results of this paper are used along with previous results of the authors to construct novel MPCs arising from σ , δ -codes. Some properties of such constructions are also studied.

scholarly journals New quantum codes from evaluation and matrix-product codes

2015 ◽  
Vol 36 ◽  
pp. 98-120 ◽  
Author(s):  
Carlos Galindo ◽  
Fernando Hernando ◽  
Diego Ruano
Keyword(s):  
Quantum Codes ◽  
Matrix Product ◽  
Product Codes

New quantum codes from matrix-product codes over small fields

2020 ◽  
Vol 19 (8) ◽  
Author(s):  
Hao Song ◽  
Ruihu Li ◽  
Yang Liu ◽  
Guanmin Guo
Keyword(s):  
Quantum Codes ◽  
Matrix Product ◽  
Product Codes ◽  
Small Fields

scholarly journals DECODING OF MATRIX-PRODUCT CODES

2013 ◽  
Vol 12 (04) ◽  
pp. 1250185 ◽  
Author(s):  
FERNANDO HERNANDO ◽  
DIEGO RUANO
Keyword(s):  
Error Correction ◽  
Linear Code ◽  
Minimum Distance ◽  
Matrix Product ◽  
Decoding Algorithm ◽  
Product Codes ◽  
Error Correction Capability

We propose a decoding algorithm for the (u | u + v)-construction that decodes up to half of the minimum distance of the linear code. We extend this algorithm for a class of matrix-product codes in two different ways. In some cases, one can decode beyond the error-correction capability of the code.

Construction of Quantum Codes From Matrix-Product Codes

2020 ◽  
Vol 24 (4) ◽  
pp. 706-710
Author(s):  
Meng Cao ◽  
Haoxu Wang ◽  
Jianlian Cui
Keyword(s):  
Quantum Codes ◽  
Matrix Product ◽  
Product Codes
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