A071802 Table in which n-th row gives exponents (in decreasing order) of lexicographically earliest primitive irreducible polynomial of degree n over GF(2).

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

Offset: 1

Author

N. J. A. Sloane, Jun 24 2002

Keywords

• nonn
• nice
• easy
• tabf

Examples

			x+1, x^2+x+1, x^3+x+1, x^4+x+1, x^5+x^2+1, ...
		

References

• 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.

Crossrefs

Cf. A058943.

Programs

Mathematica

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]

Extensions

Extended by Robert G. Wilson v, Jun 25 2002