A128902 Number of degree n polynomials over GF(2) (with nonzero constant term) at Hamming distance 2 from some irreducible polynomial.

0, 0, 0, 1, 2, 7, 14, 34, 72, 157, 326, 689, 1418, 2935, 6010, 12304, 25058, 51004, 103478, 209767, 424430, 858019, 1732430, 3495434, 7046432, 14196421, 28583424, 57522469, 115704938, 232645189, 467597246, 939526144

Offset

1,5

Links

Table of n, a(n) for n=1..32.

G. Lee, F. Ruskey and A. Williams, Hamming distance from irreducible polynomials over GF(2)

Example

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.

Crossrefs

Sequence in context: A290682 A000147 A334069 * A227213 A319455 A060552

Adjacent sequences: A128899 A128900 A128901 * A128903 A128904 A128905

Keyword

nonn

Author

Frank Ruskey, Apr 22 2007

Status

approved