|
|
A071802
|
|
Table in which n-th row gives exponents (in decreasing order) of lexicographically earliest primitive irreducible polynomial of degree n over GF(2).
|
|
0
|
|
|
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;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
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.
|
|
LINKS
|
|
|
EXAMPLE
|
x+1, x^2+x+1, x^3+x+1, x^4+x+1, x^5+x^2+1, ...
|
|
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]
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice,easy,tabf
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|