Research Article

Recursive Polynomial Sets and Their Some Algebraic Applications

Volume: 46 Number: 2 June 30, 2025
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Recursive Polynomial Sets and Their Some Algebraic Applications

Abstract

This paper primarily defines the framework for a new class of polynomial sets over a finite field GF (2), providing a recursive definition and delving into pertinent algebraic properties. We also studied some applications of the obtained polynomial classes on coding theory, such as obtaining new code classes. Our focus lies on polynomial sets with degrees equal to or less than n, for which we present a methodology for encoding and decoding utilizing an irreducible polynomial p(x) = xm+xs+1, (m = 2n-1). Furthermore, as an application of this method in coding theory, we created new code classes and studied some features of these codes.

Keywords

References

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Details

Primary Language

English

Subjects

Algebra and Number Theory

Journal Section

Research Article

Authors

Publication Date

June 30, 2025

Submission Date

July 30, 2024

Acceptance Date

March 12, 2025

Published in Issue

Year 2025 Volume: 46 Number: 2

DOI

https://doi.org/10.17776/csj.1524109

IZ

https://izlik.org/JA74DT55YK

Cite

RIS / Bibtex
APA
Aktaş, H. (2025). Recursive Polynomial Sets and Their Some Algebraic Applications. Cumhuriyet Science Journal, 46(2), 405-409. https://doi.org/10.17776/csj.1524109

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