11 research outputs found
Geometric Goppa codes on Fermat curves
We consider a class of codes defined by Goppa鈥檚 algebraic-geometric construction on Fermat curves. Automorphisms and decoding of such codes are investigated
Locally recoverable codes from rational maps
Producci贸n Cient铆ficaWe give a method to construct Locally Recoverable Error-Correcting codes.
This method is based on the use of rational maps between affine spaces. The recovery of
erasures is carried out by Lagrangian interpolation in general and simply by one addition
in some good cases.Ministerio de Econom铆a, Industria y Competitividad ( grant MTM2015-65764-C3-1-P)Consejo Nacional de Desarrollo Cient铆fico y Tecnol贸gico- Brasil (grants 159852/2014-5 / 201584/2015-8
An Introduction to Algebraic Geometry codes
We present an introduction to the theory of algebraic geometry codes.
Starting from evaluation codes and codes from order and weight functions,
special attention is given to one-point codes and, in particular, to the family
of Castle codes
ON THE ORDER BOUNDS FOR ONE-POINT AG CODES
The order bound for the minimum distance of algebraic geometry codes was originally defined for the duals of one-point codes and later generalized for arbitrary algebraic geometry codes. Another bound of order type for the minimum distance of general linear codes, and for codes from order domains in particular, was given in [1]. Here we investigate in detail the application of that bound to one-point algebraic geometry codes, obtaining a bound d* for the minimum distance of these codes. We establish a connection between d* and the order bound and its generalizations. We also study the improved code constructions based on d*. Finally we extend d* to all generalized Hamming weights.53489504Danish National Science Research Council [FNV-21040368]Danish FNU [272-07-0266]Junta de CyL [VA065A07]Spanish Ministry for Science and Technology [MTM-2007-66842-C02-01, MTM 2007-64704]Aalborg UniversityThe Technical University of DenmarkDanish National Science Research Council [FNV-21040368]Danish FNU [272-07-0266]Junta de CyL [VA065A07]Spanish Ministry for Science and Technology [MTM-2007-66842-C02-01, MTM 2007-64704
New examples of maximal curves with low genus
We investigate the Jacobian decomposition of some algebraic curves over
finite fields with genus , and . As a corollary, explicit equations
for curves that are either maximal or minimal over the finite field with
elements are obtained for infinitely many 's. Lists of small 's for which
maximality holds are provided. In some cases we describe the automorphism group
of the curve