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Search: id:A071802
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| A071802 |
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Table in which n-th row gives exponents (in decreasing order) of lexicographically earliest primitive irreducible polynomial of degree n over GF(2). |
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+0
1
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| 1, 0, 2, 1, 0, 3, 1, 0, 4, 1, 0, 5, 2, 0, 6, 1, 0, 7, 1, 0, 8, 4, 3, 1, 0, 9, 1, 0, 10, 3, 0, 11, 2, 0, 12, 3, 0, 13, 4, 3, 1, 0, 14, 5, 0, 15, 1, 0, 16, 5, 3, 1, 0, 17, 3, 0, 18, 3, 0, 19, 5, 2, 1, 0, 20, 3, 0, 21, 2, 0, 22, 1, 0, 23, 5, 0, 24, 4, 3, 1, 0, 25, 3, 0, 26, 4, 3, 1, 0, 27, 5, 2, 1, 0
(list; graph; listen)
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OFFSET
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1,3
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REFERENCES
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F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier/North Holland, 1978, p. 408.
M. Olofsson, VLSI Aspects on Inversion in Finite Fields, Dissertation No. 731, Dept Elect. Engin., Linkoping, Sweden, 2002.
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EXAMPLE
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x+1, x^2+x+1, x^3+x+1, x^4+x+1, x^5+x^2+1, ...
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MATHEMATICA
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a = {}; Do[k = 2^n + 1; While[s = Apply[Plus, IntegerDigits[k, 2]*x^Table[i, {i, n, 0, -1}]]; k < 2^(n + 1) - 1 && Factor[s, Modulus -> 2] =!= s, k += 2]; a = Append[a, Reverse[ Exponent[ Apply[ Plus, IntegerDigits[k, 2]*x^Table[i, {i, n, 0, -1}]], x, List]]], {n, 1, 27}]; Flatten[a]
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CROSSREFS
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Cf. A058943.
Sequence in context: A117362 A113214 A029323 this_sequence A110355 A029293 A167192
Adjacent sequences: A071799 A071800 A071801 this_sequence A071803 A071804 A071805
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KEYWORD
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nonn,nice,easy,tabf
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 24 2002
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EXTENSIONS
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Extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 25 2002
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