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

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]