Minimum weight codewords in dual Algebraic-Geometric codes from the Giulietti-Korchmáros curve

نویسندگان

  • Daniele Bartoli
  • Matteo Bonini
چکیده

In this paper we investigate the number of minimum weight codewords of some dual AlgebraicGeometric codes associated with the Giulietti-Korchmáros maximal curve, by computing the maximal number of intersections between the Giulietti-Korchmáros curve and lines, plane conics and plane cubics.

برای دانلود رایگان 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

The dual geometry of Hermitian two-point codes

In this paper we study the algebraic geometry of any two-point code on the Hermitian curve and reveal the purely geometric nature of their dual minimum distance. We describe the minimum-weight codewords of many of their dual codes through an explicit geometric characterization of their supports. In particular, we show that they appear as sets of collinear points in many cases.

متن کامل

On the minimum distance and the minimum weight of Goppa codes from a quotient of the Hermitian curve

In this paper we study evaluation codes arising from plane quotients of the Hermitian curve, defined by affine equations of the form yq + y = xm, q being a prime power and m a positive integer which divides q+ 1. The dual minimum distance and minimum weight of such codes are studied from a geometric point of view. In many cases we completely describe the minimum-weight codewords of their dual c...

متن کامل

Notes on Algebraic-geometric Codes

Ideas from algebraic geometry became useful in coding theory after Goppa’s construction [8]. He had the beautiful idea of associating to a curve X defined over Fq, the finite field with q elements, a code C. This code, called Algebraic-Geometric (AG) code, is constructed from two divisors D and G on X , where one of them, say D, is the sum of n distinct Fq-rational points of X . It turns out th...

متن کامل

On the geometry of small weight codewords of dual algebraic geometric codes

We investigate the geometry of the support of small weight codewords of dual algebraic geometric codes on smooth complete intersections by applying the powerful tools recently developed by Alain Couvreur. In particular, by restricting ourselves to the case of Hermitian codes, we recover and extend previous results obtained by the second named author joint with Marco Pellegrini and Massimiliano ...

متن کامل

On the duals of geometric Goppa codes from norm-trace curves

In this paper we study the dual codes of a wide family of evaluation codes on norm-trace curves. We explicitly find out their minimum distance and give a lower bound for the number of their minimum-weight codewords. A general geometric approach is performed and applied to study in particular the dual codes of onepoint and two-point codes arising from norm-trace curves through Goppa’s constructi...

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

عنوان ژورنال:
  • CoRR

دوره abs/1802.03359  شماره 

صفحات  -

تاریخ انتشار 2018