Artin-Schreier Curves, Exponential Sums, and Coding Theory

نویسنده

  • Gilles Lachaud
چکیده

Lachaud, G., Artin-Schreier curves, exponential sums, and coding theory, Theoretical Computer Science 94 (1992) 295-310. This is a survey of some results recently obtained on the distribution of the weights of some classical linear codes on the one hand, such as the dual of the Melas code, and the geometric BCH codes discovered by Goppa (subfield subcodes of Goppa codes) on the other hand. These results depend upon the properties of certain algebraic curves defined over a finite field, and the associated exponential sums, such as the Kloosterman sums.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Using Quadratic Forms to find Curves with Many Points

In both algebraic geometry and coding theory, there is a great deal of interest in finding curves with many rational points. In particular, the correspondence between trace codes and Artin-Schreier curves gives a relation between the weights of codewords and the number of rational points on such curves, low weight codewords yielding curves with a large number of rational points. Further, subcod...

متن کامل

Universal Hashing and Geometric Codes

We describe a new application of algebraic coding theory to universal hashing and authentication without secrecy. This permits to make use of the hitherto sharpest weapon of coding theory, the construction of codes from algebraic curves. We show in particular how codes derived from Artin-Schreier curves, Hermitian curves and Suzuki curves yield classes of universal hash functions which are subs...

متن کامل

Hodge-stickelberger Polygons for L-functions of Exponential Sums

Let Fq be a finite field of cardinality q and characteristic p. Let P (x) be any one-variable Laurent polynomial over Fq of degree (d1, d2) respectively and p d1d2. For any fixed s ≥ 1 coprime to p, we prove that the q-adic Newton polygon of the L-functions of exponential sums of P (xs) has a tight lower bound which we call Hodge-Stickelberger polygon, depending only on the d1, d2, s and the re...

متن کامل

HODGE-STICKELBERGER POLYGONS FOR L-FUNCTIONS OF EXPONENTIAL SUMS OF P (x)

Let Fq be a finite field of cardinality q and characteristic p. Let P (x) be any one-variable Laurent polynomial over Fq of degree (d1, d2) respectively and p d1d2. For any fixed s ≥ 1 coprime to p, we prove that the q-adic Newton polygon of the L-functions of exponential sums of P (xs) has a tight lower bound which we call HodgeStickelberger polygon, depending only on the d1, d2, s and the res...

متن کامل

Complete arcs arising from a generalization of the Hermitian curve (extended abstract)

We investigate complete arcs of degree greater than two, in projective planes over finite fields, arising from the set of rational points of a generalization of the Hermitian curve. The degree of the arcs is closely related to the number of rational points of a class of Artin–Schreier curves which is calculated by using exponential sums via Coulter’s approach. We also single out some examples o...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Theor. Comput. Sci.

دوره 94  شماره 

صفحات  -

تاریخ انتشار 1992