T. Beth, W. Geiselmann and F. Meyer, `Finding (good) normal bases in finite fields', Proc. Internat. Symp. on Symbolic and Algebraic Comp., 1991, 173--178.  Home/Search   Document Not in Database   Summary   Related Articles

....periods generate a primitive normal basis as well. This numerical evidence has a partial theoretic confirmation in [27] where an exponential lower bound is proved for some special Gauss periods. Actually the theory of Gauss periods (especially of order 2) entered this subject from the works [2] [3], 24] 61] 62] and others where the notion of complexity of a basis is introduced. More exactly, let ff generate a normal basis of F q n over F q with the multiplication table ff q i ff q j = n Gamma1 X k=0 (k) ij ff q k ; 0 i; j n Gamma 1: Fix any k = 0; 1; n ....

....the general case, nothing better than the trivial bound C(n; q) n 2 is known. Conjecture 11. C(n; q) o(n 2 ) for any q and n 1. Conjecture 11 may be very difficult because it is related to such deep number theoretic questions as Artin s conjecture and the Tchebotarev Density Theorem (see [3] and [23] However we are much more optimistic about the same question if we consider the weaker: Problem 12. Prove that for any fixed q, C(n; q) o(n 2 ) for any infinite set of n with asymptotic density 1. A similar question can be asked about normal bases (over F p ) whose multiplication ....

T. Beth, W. Geiselmann and F. Meyer, `Finding (good) normal bases in finite fields', Proc. Internat. Symp. on Symbolic and Algebraic Comp., 1991, 173--178.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC