The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A042982

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A042982

Number of degree-n irreducible polynomials over GF(2) with trace = 1 and subtrace = 1.
(history; published version)

#35 by Alois P. Heinz at Tue Apr 30 12:02:15 EDT 2019

STATUS

proposed

approved

#34 by Michel Marcus at Tue Apr 30 10:49:11 EDT 2019

STATUS

editing

proposed

#33 by Michel Marcus at Tue Apr 30 10:48:58 EDT 2019

CROSSREFS

Cf. A042979-A042982, A042980, A042981.

Cf. A074027-, A074028, A074029, A074030.

STATUS

proposed

editing

#32 by Torsten Muetze at Tue Apr 30 10:43:06 EDT 2019

STATUS

editing

proposed

#31 by Torsten Muetze at Tue Apr 30 10:43:01 EDT 2019

LINKS

F. Ruskey, <a href="http://www.theory.cs.uviccombos.ca/~cos/inf/neckorg/TraceSubtracePoly.htmlTSpoly">Number of irreducible polynomials over GF(2) with given trace and subtrace</a>

STATUS

approved

editing

Discussion

Tue Apr 30

10:43

Torsten Muetze: Repaired broken link

#30 by Giovanni Resta at Sun Aug 19 02:53:17 EDT 2018

STATUS

reviewed

approved

#29 by Joerg Arndt at Sun Aug 19 02:47:05 EDT 2018

STATUS

proposed

reviewed

#28 by Michel Marcus at Sun Aug 19 02:29:37 EDT 2018

STATUS

editing

proposed

#27 by Michel Marcus at Sun Aug 19 02:29:33 EDT 2018

REFERENCES

K. Cattell, C. R. Miers, F. Ruskey, J. Sawada and M. Serra, "The Number of Irreducible Polynomials over GF(2) with Given Trace and Subtrace", J. Comb. Math. and Comb. Comp., 47 (2003) 31-64.

LINKS

K. Cattell, C. R. Miers, F. Ruskey, J. Sawada and M. Serra, <a href="https://www.researchgate.net/publication/2634456_The_Number_of_Irreducible_Polynomials_over_GF2_with_Given_Trace_and_Subtrace">The Number of Irreducible Polynomials over GF(2) with Given Trace and Subtrace</a>, J. Comb. Math. and Comb. Comp., 47 (2003) 31-64.

FORMULA

a(n) = (1/n) * Sum_{ L(n, k) : n+k = 3 mod 4}, where L(n, k) = Sum_{ mu(d)*{binomial(n/d choose , k/d} ) : d|gcd(n, k)}.

STATUS

proposed

editing

#26 by Jon E. Schoenfield at Sat Aug 18 18:14:56 EDT 2018

STATUS

editing

proposed