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Search: id:A064390
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| A064390 |
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Numbers of the form 2^k*(2^n+1) or 2^k*(4^n-2^n+1). |
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2
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| 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
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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.
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REFERENCES
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J. F. Dillon, Geometry, codes and difference sets: exceptional connections, in Codes and designs (Columbus, OH, 2000), pp. 73-85, de Gruyter, Berlin, 2002.
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.
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CROSSREFS
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Cf. A064386.
Sequence in context: A065108 A094563 A068095 this_sequence A080671 A124455 A072378
Adjacent sequences: A064387 A064388 A064389 this_sequence A064391 A064392 A064393
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Sep 28 2001
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