Recurrent algorithm for calculation of value of formal derivative of polynomial over Galois field and its hardware implementation

Within the scope of this scientific paper the formal derivative of the polynomial over the Galois field GF(pm) and a formula for calculation of the formal derivative are considered. Calculation of the formal derivative of the polynomial is used in the decoding algorithm of the information frames dur...

Full description

Saved in:
Bibliographic Details
Published in:Journal of physics. Conference series 2019-10, Vol.1333 (3), p.32067
Main Author: Rahman, P A
Format: Article
Language:English
Subjects:
Algorithms
Codes
Data transmission
Decoding
Hardware
Mathematical analysis
Physics
Polynomials
Redundancy
Reed-Solomon codes
Scientific papers
Storage systems
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Within the scope of this scientific paper the formal derivative of the polynomial over the Galois field GF(pm) and a formula for calculation of the formal derivative are considered. Calculation of the formal derivative of the polynomial is used in the decoding algorithm of the information frames during application of the Reed-Solomon codes, which are widely used in the data transmission and storage systems with the data redundancy. The definition of the formal derivative of polynomial over the Galois field GF(pm) and the recurrent algorithm offered by the author for calculation of the value of the formal derivative of the polynomial over the Galois field GF(pm) with a given argument are also presented. Finally, the hardware implementation of the offered calculation scheme for the case of binary Galois field GF(2m) is also given.
ISSN:1742-6588
1742-6596
DOI:10.1088/1742-6596/1333/3/032067