The Degrees of Lifts of Curves and Exponential Sums over Galois Rings
نویسنده
چکیده
In this paper, we are interested in giving bounds for exponential sums over certain curves defined over Galois rings. We first define summation subsets as the images of lifts of affine pieces of the reduced curve, and most of the work is devoted to giving bounds for the degrees of their defining functions. Then we get bounds for exponential sums, generalizing results of Kumar et al., Winnie Li over the projective line, and Voloch-Walker over elliptic curves and Cab curves.
منابع مشابه
Lifts of Points on Curves and Exponential Sums
We give bounds for exponential sums over curves defined over Galois rings. We first define summation subsets as the images of lifts of points from affine opens of the reduced curve, and give bounds for the degrees of their coordinate functions. Then we get bounds for exponential sums, extending results of Kumar et al., Winnie Li over the projective line, and Voloch-Walker over elliptic curves a...
متن کاملEuclidean Weights of Codes from Elliptic Curves over Rings
We construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools, notably an estimate for certain exponential sums and some results on canonical lifts of elliptic curves. These results may be of independent interest.
متن کاملUniversal Hash Functions from Exponential Sums over Finite Fields and Galois Rings
In t#liis 1)apcr ncw families o f stmngly universal hash funct,ions, or equivalently, authentication codes, are proposed. Their parameters are derived from bounds on exponential sums over finite fields and Galois rings. This is the first tirnr hash families based upon such exponential sums have 1)een considered. Thi>ir performance improves the previously best known c.oiist,ructions and they rai...
متن کاملHomogeneous Weights and Exponential Sums
In this paper, we give a formula as an exponential sum for a homogeneous weight defined by Constantinescu and Heise [3] in the case of Galois rings (or equivalently, rings of Witt vectors) and use this formula to estimate the weight of codes obtained from algebraic geometric codes over rings.
متن کاملLarge Family of Sequences from Elliptic Curves over Residue Class Rings
SUMMARY An upper bound is established for certain exponential sums on the rational points of an elliptic curve over a residue class ring Z N , N = pq for two distinct odd primes p and q. The result is a generalization of an estimate of exponential sums on rational point groups of elliptic curves over finite fields. The bound is applied to showing the pseudoran-domness of a large family of binar...
متن کامل