Quantum error-correcting codes from Algebraic Geometry codes of Castle type
نویسندگان
چکیده
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.
منابع مشابه
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 کاملQuantum 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 کاملConstacyclic Codes over Group Ring (Zq[v])/G
Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...
متن کاملNonbinary quantum error-correcting codes from algebraic curves
We give a generalized CSS construction for nonbinary quantum error-correcting codes. Using this we construct nonbinary quantum stabilizer codes from algebraic curves. We also give asymptotically good nonbinary quantum codes from a GarciaStichtenoth tower of function fields which are constructible in polynomial time. keywords Algebraic geometric codes, nonbinary quantum codes.
متن کاملSome good quantum error-correcting codes from algebraic-Geometric codes
It is shown that the quantum error-correction can be acheived by the using of classical binary codes or additive codes over F4 (see [1],[2],[3]). In this paper with the help of some algebraic techniques the theory of algebraic-geometric codes is used to construct asymptotically good family of quantum error-correcting codes and other classes of good quantum error-correcting codes. Our results ar...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Quantum Information Processing
دوره 15 شماره
صفحات -
تاریخ انتشار 2016