Algebraic Geometry Codes from Castle Curves

نویسندگان

  • Carlos Munuera
  • Alonso Sepúlveda
  • Fernando Torres
چکیده

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.

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

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

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

Castle curves and codes

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.

متن کامل

Quantum codes from superelliptic curves

Let X be an algebraic curve of genus g ≥ 2 defined over a field Fq of characteristic p > 0. From X , under certain conditions, we can construct an algebraic geometry code CX . When this code (or its dual) is self-orthogonal under the symplectic product, a quantum algebraic geometry code QX is constructed. In this paper we study the construction of such codes from curves with automorphisms and t...

متن کامل

Construction and decoding of a class of algebraic geometry codes

Absfruct We construct a class of codes derived from algebraic plane curves. The concepts and results from algebraic geometry we use are explained in detail, and no further knowledge of algebraic geometry is needed. Parameters, generator and parity-check matrices are given. The main result is a decoding algorithm which turns out to be a generalization of the Peterson algorithm for decoding BCH c...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2008