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Bi-Unitary Superperfect Polynomials over 2 with at Most Two Irreducible Factors.

Authors :
Chehade, Haissam
Miari, Domoo
Alkhezi, Yousuf
Source :
Symmetry (20738994); Dec2023, Vol. 15 Issue 12, p2134, 10p
Publication Year :
2023

Abstract

A divisor B of a nonzero polynomial A, defined over the prime field of two elements, is unitary (resp. bi-unitary) if g c d (B , A / B) = 1 (resp. g c d u (B , A / B) = 1) , where g c d u (B , A / B) denotes the greatest common unitary divisor of B and A / B . We denote by σ * * (A) the sum of all bi-unitary monic divisors of A. A polynomial A is called a bi-unitary superperfect polynomial over F 2 if the sum of all bi-unitary monic divisors of σ * * (A) equals A. In this paper, we give all bi-unitary superperfect polynomials divisible by one or two irreducible polynomials over F 2 . We prove the nonexistence of odd bi-unitary superperfect polynomials over F 2 . [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
20738994
Volume :
15
Issue :
12
Database :
Complementary Index
Journal :
Symmetry (20738994)
Publication Type :
Academic Journal
Accession number :
174464145
Full Text :
https://doi.org/10.3390/sym15122134