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A132453 First primitive GF(2)[X] polynomial of degree n and minimal number of terms. 4


%S 3,7,11,19,37,67,131,285,529,1033,2053,4179,8219,16427,32771,65581,

%T 131081,262273,524327,1048585,2097157,4194307,8388641,16777243,

%U 33554441,67108935,134217767,268435465,536870917,1073741907,2147483657

%N First primitive GF(2)[X] polynomial of degree n and minimal number of terms.

%C More precisely: minimum value for X=2 of primitive GF(2)[X] polynomials of degree n and minimal number of terms for such polynomials. Applications include maximum-length linear feedback shift registers with efficient implementation in both hardware and software.

%H J. Arndt, <a href="http://www.jjj.de/mathdata/minweight-primpoly.txt">Polynomials as lists of coefficients for 2<=n<=400</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>

%H <a href="/index/Tri#trinomial">Index entries for sequences related to trinomials over GF(2)</a>

%e a(10)=1033, or 10000001001 in binary, representing the GF(2)[X] polynomial X^10+X^3+1, because this polynomial has degree 10, it has 3 terms and no degree 10 polynomial with less terms than that is primitive and it is primitive, contrary to X^10+X^1+1, X^10+X^2+1 and X^10+X^2+X^1.

%Y Subset of A091250. A132454(n) encodes a(n) in a more compact representation. Cf. A132447, similar with no restriction on number of terms. Cf. A132449, similar with restriction to at most 5 terms. Cf. A132451, similar with restriction to exactly 5 terms.

%K nonn

%O 1,1

%A Francois R. Grieu (f(AT)grieu.com), Aug 22 2007

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Last modified August 24 22:49 EDT 2019. Contains 326314 sequences. (Running on oeis4.)