一种新的长度可分的量子MDS编码 \(q^w-1\)

IF 2.2 3区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Quantum Information Processing Pub Date : 2025-08-19 DOI:10.1007/s11128-025-04900-9

Fu-Yu Gu, Rui Wang, Yi Li, Ming-Qiang Bai

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引用次数: 0

摘要

通过应用厄密构造方法，通过恒环码成功地开发了大量量子最大距离可分码。虽然现有的量子纠错码（QECCs）通常以长度为\(q^w-1\)的因数为特征，其中q是素数幂，w表示正偶数，但这项工作引入了一个新的量子MDS码族，其长度除\(q^w-1\)，其中w是奇数素数。这些代码的长度超过\(q + 1\)，最小距离大于\(\frac{q}{2}+1\)。此外，还给出了\(w=3\)的两个特定量子MDS代码。

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A family of new quantum MDS codes with lengths dividing \(q^w-1\)

A significant number of quantum maximal-distance-separable (MDS) codes have been successfully developed via constacyclic codes through the application of the Hermitian construction method. While existing quantum error-correcting codes (QECCs) often feature lengths that are divisors of \(q^w-1\), with q being a prime power and w representing a positive even number, this work introduces a novel family of quantum MDS codes with lengths dividing \(q^w-1\), where w is instead an odd prime number. These codes have lengths exceeding \(q + 1\) and minimum distances larger than \(\frac{q}{2}+1\). Additionally, two specific quantum MDS codes for \(w=3\) are presented.

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来源期刊

Quantum Information Processing 物理-物理：数学物理

CiteScore

4.10

自引率

20.00%

发文量

337

审稿时长

4.5 months

期刊介绍： Quantum Information Processing is a high-impact, international journal publishing cutting-edge experimental and theoretical research in all areas of Quantum Information Science. Topics of interest include quantum cryptography and communications, entanglement and discord, quantum algorithms, quantum error correction and fault tolerance, quantum computer science, quantum imaging and sensing, and experimental platforms for quantum information. Quantum Information Processing supports and inspires research by providing a comprehensive peer review process, and broadcasting high quality results in a range of formats. These include original papers, letters, broadly focused perspectives, comprehensive review articles, book reviews, and special topical issues. The journal is particularly interested in papers detailing and demonstrating quantum information protocols for cryptography, communications, computation, and sensing.