Xianmang He, Zusheng Zhang, Si Tian, Jingli Wang, Yindong Chen
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引用次数: 0
摘要
在过去的十年中，学术界一直在追求恒维编码（简称 CDC）的心度改进。Lao 等人（IEEE Trans Inf Theory 69(7):4333-4344, 2023）指出，混合维度子空间编码可用于构造大型恒维子空间编码。对 CDC 构建的探索转化为寻找具有大维分布的混合维/距离子空间码。在本文中，我们将并行构造应用于这种混合维度构造，从而贡献了大约 80 多个新的常维码。
Parallel construction for constant dimension codes from mixed dimension construction
The community has been pursuing improvements in the cardinalities for constant dimensional codes (CDC for short) for the past decade. Lao et al. (IEEE Trans Inf Theory 69(7):4333–4344, 2023) has shown that mixed dimension subspace codes can be used to construct large constant dimension subspace codes. The exploration of the CDCs’ construction is transformed into finding mixed dimension/distance subspace codes with large dimension distributions. In this paper, we apply the parallel construction to this mixed dimension construction, which allows us to contribute approximately more than 80 new constant dimension codes.
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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