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Number of degree n polynomials over GF(2) (with nonzero constant term) at Hamming distance 2 from some irreducible polynomial.
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%I #5 Aug 10 2015 00:03:41

%S 0,0,0,1,2,7,14,34,72,157,326,689,1418,2935,6010,12304,25058,51004,

%T 103478,209767,424430,858019,1732430,3495434,7046432,14196421,

%U 28583424,57522469,115704938,232645189,467597246,939526144

%N Number of degree n polynomials over GF(2) (with nonzero constant term) at Hamming distance 2 from some irreducible polynomial.

%H G. Lee, F. Ruskey and A. Williams, <a href="http://www.cs.uvic.ca/~ruskey/Publications/DistGF2/DistGF2.html">Hamming distance from irreducible polynomials over GF(2)</a>

%e 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.

%K nonn

%O 1,5

%A _Frank Ruskey_, Apr 22 2007