1,2

More precisely: minimum value for X=2 of GF(2)[X] polynomials P[X] with at most 4 terms such that X^n+P[X] is primitive. Applications include maxmimum-length linear feedback shift registers with efficient implementation in both hardware and software. The limitation of the number of terms occurs first for a(32), which is 197 representing X^7+X^6+X^2+1, rather than 175 representing X^7+X^5+X^3+X^2+X^1+1. Proof is needed that there exists a primitive GF(2)[X] polynomial P[X] of degree n and at most 5 terms for all positive n.

Index entries for sequences operating on GF(2)[X]-polynomials

a(11)=5, or 101 in binary, representing the GF(2)[X] polynomial X^2+1, because X^11+X^2+1 has no more than 5 terms, and X is primitive, contrary to X^11, X^11+1, X^11+X^1, X^11+X^1+1, and X^11+X^2.

A132450 2^n+a(n) belongs to A091250. A132449(n) = a(n)+2^n and gives the corresponding primitive polynomial. Cf. A132448, similar with no restriction on number of terms. Cf. A132452, similar with restriction to exactly 5 terms.

Sequence in context: A075018 A125958 A132448 this_sequence A132424 A070864 A076566

Adjacent sequences: A132447 A132448 A132449 this_sequence A132451 A132452 A132453

more,nonn

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