Structure of CSS and CSS-T quantum codes

IF 1.4 2区 数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Designs, Codes and Cryptography Pub Date : 2024-05-24 DOI:10.1007/s10623-024-01415-9
Elena Berardini, Alessio Caminata, Alberto Ravagnani
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Abstract

We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of linear codes that give rise to a CSS code with good correction capability, showing that such pairs are easy to produce with a randomized construction. We then prove that CSS-T codes exhibit the opposite behaviour, showing also that, under very natural assumptions, their rate and relative distance cannot be simultaneously large. This partially answers an open question on the feasible parameters of CSS-T codes. We conclude with a simple construction of CSS-T codes from Hermitian curves. The paper also offers a concise introduction to CSS and CSS-T codes from the point of view of classical coding theory.

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CSS 和 CSS-T 量子编码的结构
我们从 CSS 和 CSS-T 量子纠错码的存在性、稀有性和性能的角度对它们进行了研究。我们给出了能产生具有良好纠错能力的 CSS 码的线性码对数量的下限,并表明通过随机构造很容易产生这样的码对。然后,我们证明了 CSS-T 编码表现出相反的行为,并表明在非常自然的假设条件下,它们的速率和相对距离不可能同时很大。这部分回答了关于 CSS-T 编码可行参数的一个未决问题。最后,我们用赫尔墨斯曲线简单构建了 CSS-T 编码。本文还从经典编码理论的角度简要介绍了 CSS 和 CSS-T 编码。
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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来源期刊
Designs, Codes and Cryptography
Designs, Codes and Cryptography 工程技术-计算机:理论方法
CiteScore
2.80
自引率
12.50%
发文量
157
审稿时长
16.5 months
期刊介绍: Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines. The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome. The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas. Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.
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