A064390 Numbers of the form 2^k*(2^n+1) or 2^k*(4^n-2^n+1).

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 16, 17, 18, 20, 24, 26, 32, 33, 34, 36, 40, 48, 52, 57, 64, 65, 66, 68, 72, 80, 96, 104, 114, 128, 129, 130, 132, 136, 144, 160, 192, 208, 228, 241, 256, 257, 258, 260, 264, 272, 288, 320, 384, 416, 456, 482, 512

Offset

1,2

Comments

Call m exceptional if the binary cyclic code of length 2^k-1 with zeros w and w^m (w primitive in GF(2^k)) is double-error-correcting for infinitely many k. It is conjectured that this sequence (with the powers of 2 omitted) gives all exceptional m's.

References

J. F. Dillon, Geometry, codes and difference sets: exceptional connections, in Codes and designs (Columbus, OH, 2000), pp. 73-85, de Gruyter, Berlin, 2002.

Links

Table of n, a(n) for n=1..58.

H. Janwa, G. McGuire and R. M. Wilson, Double-error-correcting codes and absolutely irreducible polynomials over GF(2), J. Algebra, 178 (1995), 665-676.

Crossrefs

Cf. A064386.

Sequence in context: A094563 A228897 A068095 * A229461 A230709 A080671

Adjacent sequences: A064387 A064388 A064389 * A064391 A064392 A064393

Keyword

nonn

Author

N. J. A. Sloane, Sep 28 2001

Status

approved