Introduction to finite fields and their applications
Introduction to finite fields and their applications
Constructive problems for irreducible polynomials over finite fields
Proceedings of the third Canadian workshop on Information theory and applications
Construction and distribution problems for irreducible trinomials over finite fields
Applications of finite fields
New primitive t-nomials (t&equil;3,5) over GF(2) whose degree is a Mersenne exponent
Mathematics of Computation
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Shift Register Sequences
Random Number Generation and Simulation on Vector and Parallel Computers
Euro-Par '98 Proceedings of the 4th International Euro-Par Conference on Parallel Processing
A fast algorithm for testing irreducibility of trinomials mod 2
A fast algorithm for testing irreducibility of trinomials mod 2
Improved long-period generators based on linear recurrences modulo 2
ACM Transactions on Mathematical Software (TOMS)
Random number generators with period divisible by a Mersenne prime
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartI
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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 2r - 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 et al. The two results for r = 3021377 are primitive trinomials of the highest known degree.