On even (unitary) perfect polynomials over F2

We give all even perfect (resp. unitary perfect) polynomials over the prime field F2 of the form , where each Mi is a Mersenne irreducible polynomial, hi=2ni−1 (resp. hi=2ni) and a,b,r,ni∈N. In particular, we characterize nine of the eleven known “sporadic” even perfect polynomials over F2 that have the above form.