Asymptotically Good Quantum Codes
نویسندگان
چکیده
Using algebraic geometry codes we give a polynomial construction of quantum codes with asymptotically non-zero rate and relative distance.
منابع مشابه
Good and asymptotically good quantum codes derived from algebraic geometry codes
In this paper we construct several new families of quantum codes with good and asymptotically good parameters. These new quantum codes are derived from (classical) algebraic geometry (AG) codes by applying the Calderbank-Shor-Steane (CSS) construction. Many of these codes have large minimum distances when compared with its code length and they have relatively small Singleton defect. For example...
متن کاملAsymptotically good quantum codes exceeding the Ashikhmin-Litsyn-Tsfasman bound
Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. 2055 REFERENCES [1] G. F. M. Beenker, " A note on extended quadratic r...
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 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 کاملذخیره 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 2001