Stabilizer codes over Frobenius rings

机译：Frobenius环上的稳定剂代码

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Quantum error-correcting codes over finite fields have been widely studied, but quantum codes over rings have been left largely unexplored. This paper introduces stabilizer codes over finite Frobenius rings and establishes their connection to classical code. Structural properties of stabilizer codes over finite Frobenius rings are established. It is proved that free stabilizer codes over finite commutative chain rings cannot outperform stabilizer codes over finite fields.

机译：有限域上的量子纠错码已经得到了广泛的研究，但是环上的量子码还没有得到充分的研究。本文介绍了有限Frobenius环上的稳定器代码，并建立了它们与经典代码的联系。建立了有限Frobenius环上稳定子代码的结构性质。证明了有限交换链环上的自由稳定器代码不能超过有限域上的稳定器代码。

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《IEEE International Symposium on Information Theory;ISIT 2012》|2012年|p.165- 169|共5页
会议地点 Cambridge, MA(US)
作者
Nadella, Sushma; Klappenecker, Andreas;
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Department of Computer Science and Engineering Texas A&M University College Station Texas 77843-3112;

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2. On quantum stabilizer codes derived from local Frobenius rings [J] . Gluesing-Luerssen Heide, Pllaha Tefjol Finite fields and their applications . 2019,第Jula期

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3. Double bordered constructions of self-dual codes from group rings over Frobenius rings [J] . Gildea Joe, Taylor Rhian, Kaya Abidin, Cryptography and Communications . 2020,第4期

机译：来自Frobenius环的小组环的自我双重代码的双层建筑
4. Stabilizer codes over Frobenius rings [C] . Nadella Sushma, Klappenecker Andreas IEEE International Symposium on Information Theory . 2012

机译：Frobenius环上的稳定器代码
5. Quantum error correcting codes: From stabilizer codes to induced codes. [D] . Loeb, Edward A., III. 2006

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机译：Z形环装配中的FtsZ C末端可变区（CTV）的特征以及与大肠杆菌胞质分裂中Z形环稳定剂ZapD的相互作用
7. On quantum stabilizer codes derived from local Frobenius rings [O] . Heide Gluesing-Luerssen, Tefjol Pllaha 2019

机译：关于源自本地Frobenius环的量子稳定剂代码

Stabilizer codes over Frobenius rings

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