Castle curves and codes

نویسندگان

  • Carlos Munuera
  • Alonso Sepúlveda
  • Fernando Torres
چکیده

We introduce two types of curves of interest for coding theory purposes: the so-called Castle and weak Castle curves. We study the main properties of codes arising from these curves.

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

Algebraic Geometry Codes from Castle Curves

The quality of an algebraic geometry code depends on the curve from which the code has been defined. In this paper we consider codes obtained from Castle curves, namely those whose number of rational points attains Lewittes’ bound for some rational point Q and the Weierstrass semigroup at Q is symmetric.

متن کامل

One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...

متن کامل

Quantum error-correcting codes from Algebraic Geometry codes of Castle type

We study Algebraic Geometry codes producing quantum error-correcting codes by the CSS construction. We pay particular attention to the family of Castle codes. We show that many of the examples known in the literature in fact belong to this family of codes. We systematize these constructions by showing the common theory that underlies all of them.

متن کامل

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.

متن کامل

Diagnostic Performance and Repeatability of a Novel Game-Based Visual Field Test for Children.

Purpose To demonstrate utility of a game-based test ("Caspar's Castle") for the detection of visual field defects in children. Methods A validity and reliability study was carried out at Manchester Royal Eye Hospital Pediatric Ophthalmology Outpatients Department. We recruited 108 children with no eye pathology (aged 4-12 years) and examined a single eye with the Caspar's Castle system using ...

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:
  • Adv. in Math. of Comm.

دوره 3  شماره 

صفحات  -

تاریخ انتشار 2009