Let Fqn be an extension of the field Fq of degree n = mpl , l ≥ 1 where p is the characteristic of the field Fq . It is proved that the number of self-dual normal bases generators of Fqn over Fq in (TrFqn |Fqm ) −1(β), for any self-dual normal basis generator β of Fqm over Fq , is independent of the choice of β.

Efficient multiplication in finite fields Fqn requires Fq-bases of low density,i.e., such that the products of the basis elements have a sparse expression in the basis. In this paper we introduce a new family of bases: the quasi-normal bases. These bases generalize the notion of normal bases and provide simple exponentiation to the power q in Fqn . For some extension fields Fqn over Fq, we cons...

Let C be a smooth absolutely irreducible curve of genus g ≥ 1 defined over Fq, the finite field of q elements, and let #C(Fqn) be the number of Fqn-rational points on C. Under a certain condition, which, for example, satisfied by all ordinary elliptic curves, we obtain an asymptotic formula for the number of ratios (#C(Fqn)−q−1)/2gq, n = 1, . . . , N , inside of a given interval I ⊆ [−1, 1] . T...

Two related results are proven in the modular invariant theory of GLn(Fq ). The first is a finite field analogue of a result of Springer on coinvariants of the symmetric group Sn acting on C[x1, . . . , xn]. It asserts that the following two Fqn [GLn(Fq )×F × q ]modules have the same composition factors: • the coinvariant algebra for GLn(Fq ) acting on Fqn [x1, . . . , xn], in which GLn(Fq ) ac...

The n-dimensional folded hypercube FQn, a variation of the hypercube proposed by Ahmed et al. [A. El-Amawy, S. Latifi, Properties and performance of folded hypercubes, IEEE Transactions on Parallel and Distributed Systems 2(3) (1991) 31–42], is an (n + 1)-regular (n + 1)-connected graph. Conditional diagnosability, a new measure of diagnosability introduced by Lai et al. [Pao-Lien Lai, Jimmy J....

Let C be a smooth absolutely irreducible curve of genus g ≥ 1 defined over Fq, the finite field of q elements, and let #C(Fqn) be the number of Fqn-rational points on C. Under a certain condition, which for example, satisfied by all ordinary elliptic curves, we obtain an asymptotic formula for the number of ratios (#C(Fqn)−q−1)/2gq, n = 1, . . . , N , inside of a given interval I ⊆ [−1, 1] . Th...