**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of Graph Search.

Publication# Minimum distance of elliptic codes

Abstract

In this paper we investigate three classes of linear codes arising from elliptic curves and compute their minimal distance using implicity the structure of the group of rational points of the curves.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (52)

Related MOOCs (1)

Related concepts (32)

Ontological neighbourhood

Introduction to optimization on smooth manifolds: first order methods

Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).

Elliptic curve

In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over a field K and describes points in K^2, the Cartesian product of K with itself. If the field's characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions (x, y) for: for some coefficients a and b in K. The curve is required to be non-singular, which means that the curve has no cusps or self-intersections.

Group action

In mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group acts on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it.

Rational point

In number theory and algebraic geometry, a rational point of an algebraic variety is a point whose coordinates belong to a given field. If the field is not mentioned, the field of rational numbers is generally understood. If the field is the field of real numbers, a rational point is more commonly called a real point. Understanding rational points is a central goal of number theory and Diophantine geometry. For example, Fermat's Last Theorem may be restated as: for n > 2, the Fermat curve of equation has no other rational points than (1, 0), (0, 1), and, if n is even, (–1, 0) and (0, –1).

,

The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an analytically tractable m ...

, , ,

In a group, the collective dynamics is governed by the inter- actions between individuals, which can manifest differently depending on the available means of communication. In this paper, we compare 3 conditions of communication affordances (global chat, l ...

We give a characterization of rational points lying on the Noether-Lefschetz locus of moduli spaces of K3 surfaces by studying their lifting properties under some natural coverings of the ambient space. We then prove that the Bombieri-Lang conjecture impli ...