For any projective embedding of a non-singular irreducible complete algebraic curve defined over a finite field, we obtain an upper bound for the number of its rational points. The constants in the… Expand

LetK be a function field in one variable over ℂ anda1,...,am,b non-zero elements ofK, such thatb is linearly independent froma1,...,am over ℂ. We show that forn sufficiently large, the equation… Expand

A new, simpler technique based on bounds of character sums is presented to prove the indifferentiability of similar hash function constructions based on essentially any deterministic encoding to elliptic curves or curves of higher genus, such as the algorithms by Shallue, van de Woestijne and Ulas, or the Icart-like encodings recently presented.Expand

The main purpose of this paper is to establish a formula for the Cartier operator on a plane algebraic curve in terms of a differential operator in polynomials in two variables. This formula is very… Expand

The authors construct certain error-correcting codes over finite rings and estimate their parameters, notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves.Expand

A central time-shared data processing system organized for character analysis and coupled to a number of remote document scanning stations each including a drum document feed to produce data identifying graphic figures for analysis by the central processing system.Expand

We obtain a lower bound on the multiplicative order of Gauss periods which generate normal bases over finite fields. This bound improves the previous bound of von zur Gathen and Shparlinski.