Generic Programming Approach in the Implementation of Error-Correcting Codes From Algebraic Geometry

نویسنده

  • Artem Pelenitsyn
چکیده

We describe design decisions adopted in our software implementation of decoder for a class of algebraic geometry codes. The decisions develop methodology of generic programming and show some metaprogramming techniques which are valuable when solving similar problems from the field of error-correcting codes or more generally computational algebraic geometry. We also emphasize features of C++11 which are to increase support for generic programming in C++ language.

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

Quantum Codes from Algebraic Geometry

Quantum error correcting codes are essential for successful implementation of quantum computers. We look into the theory of a particular class of quantum codes that look promising called quantum stabilizer codes. The aim of this project is to study and construct efficient quantum stabilizer codes from algebraic geometry codes.

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

An approach to fault detection and correction in design of systems using of Turbo ‎codes‎

We present an approach to design of fault tolerant computing systems. In this paper, a technique is employed that enable the combination of several codes, in order to obtain flexibility in the design of error correcting codes. Code combining techniques are very effective, which one of these codes are turbo codes. The Algorithm-based fault tolerance techniques that to detect errors rely on the c...

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

A Graph-Theoretic Approach to Bounds for Error-Correcting Codes CIMPA-UNESCO-PHILIPPINES Summer School on Semidefinite Programming in Algebraic Combinatorics

In these notes, we address bounds for error-correcting codes. Our approach is from the viewpoint of algebraic graph theory. We therefore begin with a review of the algebraic structure of the Hamming graph, focusing on the binary case. We then derive Delsarte’s linear programming bound and explore some applications of it. In the second part of the notes, we introduce Terwilliger’s subconstituent...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012