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A132452
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First primitive GF(2)[X] polynomials of degree n with exactly 5 terms, X^n suppressed.
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5
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15, 27, 15, 29, 27, 27, 23, 83, 27, 43, 23, 45, 15, 39, 39, 83, 39, 57, 43, 27, 15, 71, 39, 83, 23, 83, 15, 197, 83, 281, 387, 387, 83, 99, 147, 57, 15, 153, 89, 101, 27, 449, 51, 657, 113, 29, 75, 75, 71, 329, 71, 149, 45, 99, 149, 53, 39, 105, 51, 27, 27, 833, 39, 163, 101, 43, 43, 1545, 29
(list; graph; refs; listen; history; internal format)
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OFFSET
| 5,1
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COMMENTS
| More precisely: minimum value for X=2 of GF(2)[X] polynomials P[X] of degree less than n and exactly 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.
Proof is needed that there exists a primitive GF(2)[X] polynomial P[X] of degree n and exactly 5 terms for all n>4.
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LINKS
| Index entries for sequences operating on GF(2)[X]-polynomials
Joerg Arndt, Table of n, a(n) for n = 5..400
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EXAMPLE
| a(11)=23, or 10111 in binary, representing the GF(2)[X] polynomial X^4+X^2+X^1+1, because X^11+X^4+X^2+X^1+1 has exactly 5 terms and it is primitive, contrary to X^11+X^3+X^2+X^1+1.
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CROSSREFS
| For n>4, 2^n+a(n) belongs to A091250. A132451(n) = a(n)+2^n and gives the corresponding primitive polynomial. Cf. A132448, similar with no restriction on number of terms. Cf. A132450, similar with restriction to at most 5 terms. Cf. A132454, similar with restriction to minimal number of terms.
Sequence in context: A097963 A063936 A205881 * A063552 A131541 A080945
Adjacent sequences: A132449 A132450 A132451 * A132453 A132454 A132455
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KEYWORD
| nonn
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AUTHOR
| Francois R. Grieu (f(AT)grieu.com), Aug 22 2007
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EXTENSIONS
| Edited and extended by Max Alekseyev (maxale(AT)gmail.com), Feb 06 2010
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