Generalized bilateral multilevel construction for constant dimension codes

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Designs, Codes and Cryptography Pub Date : 2024-11-05 DOI:10.1007/s10623-024-01513-8

Xiaoqin Hong, Xiwang Cao, Gaojun Luo

引用次数: 0

Abstract

Constant dimension codes (CDCs) have drawn extensive attention due to their applications in random network coding. This paper introduces a new class of codes, namely generalized bilateral Ferrers diagram rank-metric codes, to generalize the bilateral multilevel construction in Etzion and Vardy (Adv Math Commun 16:1165–1183, 2022). Combining our generalized bilateral multilevel construction and the double multilevel construction in Liu and Ji (IEEE Trans Inf Theory 69:157–168, 2023), we present an effective technique to construct CDCs. By means of bilateral identifying vectors, this approach helps us to select fewer identifying and inverse identifying vectors to construct CDCs with larger size. The new constructed CDCs have the largest size regarding known codes for many sets of parameters. Our method gives rise to at least 138 new lower bounds for CDCs.

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恒维代码的广义双边多级结构

常数维码（CDC）因其在随机网络编码中的应用而受到广泛关注。本文介绍了一类新码，即广义双边费勒斯图等级计量码，以推广 Etzion 和 Vardy (Adv Math Commun 16:1165-1183, 2022) 中的双边多级构造。结合我们的广义双边多级结构和 Liu 和 Ji (IEEE Trans Inf Theory 69:157-168, 2023) 中的双多级结构，我们提出了一种构建 CDC 的有效技术。通过双边识别向量，这种方法可以帮助我们选择更少的识别向量和反向识别向量来构建更大的 CDC。在许多参数集的已知代码中，新构建的 CDC 具有最大的尺寸。我们的方法为 CDC 带来了至少 138 个新下限。

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 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.