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Search: id:A132452
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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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+0
5
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| 0, 0, 0, 0, 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
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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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, or 0 if no such polynomial exists. 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
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Index entries for sequences operating on GF(2)[X]-polynomials
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EXAMPLE
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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
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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: A139566 A097963 A063936 this_sequence A063552 A131541 A080945
Adjacent sequences: A132449 A132450 A132451 this_sequence A132453 A132454 A132455
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KEYWORD
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more,nonn
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AUTHOR
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Francois R. Grieu (f(AT)grieu.com), Aug 22 2007
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