A Fast Algorithm for Testing Reducibility of Trinomials mod 2 and Some New Primitive Trinomials of Degree 3021377 - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Mathematics of Computation Year : 2003

A Fast Algorithm for Testing Reducibility of Trinomials mod 2 and Some New Primitive Trinomials of Degree 3021377

Abstract

The standard algorithm for testing reducibility of a trinomial of prime degree $r$ over $\GF(2)$ requires $2r + O(1)$ bits of memory. We describe a new algorithm which requires only $3r/2 + O(1)$ bits of memory and significantly fewer memory references and bit-operations than the standard algorithm. If $2^r-1$ is a Mersenne prime, then an irreducible trinomial of degree $r$ is necessarily primitive. We give primitive trinomials for the Mersenne exponents $r = 756839$, $859433$, and $3021377$. % The results for $r = 859433$ extend and correct some computations of Kumada {\etal}. The two results for $r = 3021377$ are primitive trinomials of the highest known degree.
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Dates and versions

inria-00099744 , version 1 (26-09-2006)

Identifiers

  • HAL Id : inria-00099744 , version 1

Cite

Richard P. Brent, Samuli Larvala, Paul Zimmermann. A Fast Algorithm for Testing Reducibility of Trinomials mod 2 and Some New Primitive Trinomials of Degree 3021377. Mathematics of Computation, 2003, 72 (243), pp.1443-1452. ⟨inria-00099744⟩
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