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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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%I #8 Mar 14 2018 03:55:19

%S 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,

%T 64,65,66,68,72,80,96,104,114,128,129,130,132,136,144,160,192,208,228,

%U 241,256,257,258,260,264,272,288,320,384,416,456,482,512

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

%C 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.

%D 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 H. Janwa, G. McGuire and R. M. Wilson, <a href="https://doi.org/10.1006/jabr.1995.1372">Double-error-correcting codes and absolutely irreducible polynomials over GF(2)</a>, J. Algebra, 178 (1995), 665-676.

%Y Cf. A064386.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Sep 28 2001