On the Dimension of Algebraic-Geometric Trace Codes
نویسندگان
چکیده
منابع مشابه
On the Construction of Algebraic-Geometric Codes
In this paper, a new view point to linear codes is presented. A concept level of linear codes is introduced and a bound of linear code’s level is given. It can be used to simplify the construction of Algebraic Geometric Codes. In particular, we define a class of codes which can be considerated as generalized RS codes and can be constructed via symbolic computation.
متن کاملAlgebraic Geometric Codes on Surfaces
— We study error-correcting codes constructed from projective surfaces over finite fields using the generalized Goppa construction. We obtain bounds for the minimal distance of these codes by understanding how the zero sets of functions on a surface decompose into irreducible components. We also present a decoding algorithm for these codes based on the Luby-Mitzenmacher algorithm for LDPC codes...
متن کاملOn the decoding of algebraic-geometric codes
This paper provides a survey of the existing literature on the decoding of algebraic-geometric codes. Definitions, theorems and cross references will be given. We show what has been done, discuss what still has to be done and pose some open problems. The following subjects are examined in a more or less historical order. 1) Introduction 2) The decoding problem 3) Algebraic-geometric codes 4) Th...
متن کاملNotes 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 کاملOn Representations of Algebraic-Geometric Codes
We show that all algebraic-geometric codes possess a succinct representation that allows for the list decoding algorithms of [9, 6] to run in polynomial time. We do this by presenting a root-finding algorithm for univariate polynomials over function fields when their coefficients lie in finite-dimensional linear spaces, and proving that there is a polynomial size representation given which the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics
سال: 2016
ISSN: 2227-7390
DOI: 10.3390/math4020032