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引用次数: 0
摘要
量子信息和量子计算已成为近几十年来的热门话题。量子纠错码非常有用，在量子计算和量子通信中有很多应用。我们构建了一类新的量子最大距离可分离（MDS）码。我们的构造基于 Ball 和 Vilar 的最新成果（IEEE Trans Inf Theory 68:3796-3805, 2022）。我们研究了一大类显式多项式，并获得了它们所需的算术性质，这意味着当 q 为奇数时，可以构造长度严格大于 \(q+1\) 的新 qary 量子 MDS 码。
New q-ary quantum MDS codes of length strictly larger than \(q+1\)
Quantum information and quantum computation have become a hot topic in recent decades. Quantum error-correcting codes are useful and have many applications in quantum computations and quantum communications. We construct a new class of quantum Maximum Distance Separable (MDS) codes. Our construction is based on a recent result of Ball and Vilar (IEEE Trans Inf Theory 68:3796–3805, 2022). We study a large class of explicit polynomials and obtain their required arithmetical properties which imply construction of new q-ary quantum MDS codes of length strictly larger than \(q+1\), when q is odd.
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.
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