Decoding Reed-Solomon Skew-Differential Codes

被引：0

作者：

Gomez-Torrecillas, Jose ^{[1
,2
]}

Navarro, Gabriel ^{[3
,4
]}

Patricio Sanchez-Hernandez, Jose ^{[2
]}

机构：

[1] Univ Granada, IMAG, Granada 18071, Spain

[2] Univ Granada, Dept Algebra, Granada 18071, Spain

[3] Univ Granada, CITIC, Granada 18071, Spain

[4] Univ Granada, Dept Comp Sci & Artificial Intelligence, Granada 18071, Spain

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2021年 / 67卷 / 12期

关键词：

Codes; Decoding; Reed-Solomon codes; Additives; Kernel; Convolutional codes; Linear codes; convolutional codes; decoding; skew codes; CONVOLUTIONAL-CODES; ALGORITHM; RANK;

D O I：

10.1109/TIT.2021.3117083

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making them fully accessible for everyone. Thus, the first part of the paper develops a direct presentation of the codes by means of parity-check matrices, and the decoding algorithm rests upon matrix and linear maps manipulations. The somewhat more sophisticated mathematical context (non-commutative rings) needed for the proof of the correctness of the decoding algorithm is postponed to the second part. A final section locates the Reed-Solomon skew-differential codes introduced here within the general context of codes defined by means of skew polynomial rings.

引用

页码：7891 / 7903

页数：13

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