Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".
A128902
Number of degree n polynomials over GF(2) (with nonzero constant term) at Hamming distance 2 from some irreducible polynomial.
The coefficient vectors of the three degree 4 irreducible polynomials are 10011, 11111 and 11001. There is only one polynomial whose Hamming distance is two (or more) from all of them, namely 10101. Thus a(4) = |{10101}| = 1.