改进最小距离的量子码

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Korean Mathematical Society Pub Date : 2019-01-01 DOI:10.4134/bkms.b180295

E. Kolotoğlu, Mustafa Sarı

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引用次数: 0

摘要

构造量子密码的方法本身并不总是足够的。此外，在经典编码理论中构造的量子码必须具有一定的参数质量，这些参数在有效地恢复数据方面起着非常重要的作用。在最近的一项研究中，La Garcia在b[14]中给出了量子结构和量子码在有限q阶域上的例子。受La Garcia论文的启发，本文通过研究在该域中构造量子码的充分必要条件，将结果推广到具有q2元的有限域。我们确定了包含至少三个元素的q2-环形共集存在的准则，并提出了量子最大距离可分离码(MDS)的构造方法。此外，我们还推导了一种构造量子码的方法，并证明了这种构造方法可以得到比[14]中的量子码具有更好参数的量子码。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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QUANTUM CODES WITH IMPROVED MINIMUM DISTANCE

The methods for constructing quantum codes is not always sufficient by itself. Also, the constructed quantum codes as in the classical coding theory have to enjoy a quality of its parameters that play a very important role in recovering data efficiently. In a very recent study quantum construction and examples of quantum codes over a finite field of order q are presented by La Garcia in [14]. Being inspired by La Garcia’s the paper, here we extend the results over a finite field with q2 elements by studying necessary and sufficient conditions for constructions quantum codes over this field. We determine a criteria for the existence of q2-cyclotomic cosets containing at least three elements and present a construction method for quantum maximum-distance separable (MDS) codes. Moreover, we derive a way to construct quantum codes and show that this construction method leads to quantum codes with better parameters than the ones in [14].

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来源期刊

Bulletin of the Korean Mathematical Society 数学-数学

CiteScore

0.80

自引率

20.00%

发文量

审稿时长

6 months

期刊介绍： This journal endeavors to publish significant research of broad interests in pure and applied mathematics. One volume is published each year, and each volume consists of six issues (January, March, May, July, September, November).