Quasi-optimum distance flag codes

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2026-06-01 Epub Date: 2026-01-15 DOI:10.1016/j.ffa.2026.102799

Clementa Alonso-González, Miguel Ángel Navarro-Pérez

引用次数: 0

Abstract

A flag is a sequence of nested subspaces of a given ambient space

F_{q}^{n}

over a finite field

F_{q}

. In network coding, a flag code is a set of flags, all of them with the same sequence of dimensions, the type vector. In this paper, we investigate quasi-optimum distance flag codes, i.e., those attaining the second best possible distance value. We characterize them and present upper bounds for their cardinality. Moreover, we propose a systematic construction for every choice of the type vector by using partial spreads and sunflowers. For flag codes with lower minimum distance, we adapt the previous construction and provide some results towards their characterization, especially in the case of the third best possible distance value.

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准最佳距离标志码

标志是给定环境空间Fqn在有限域Fq上的嵌套子空间序列。在网络编码中，标志码是一组标志，它们都具有相同的维数序列，即类型向量。在本文中，我们研究了准最优距离标志码，即那些达到次优可能距离值的标志码。我们对它们进行了表征，并给出了它们的基数的上界。此外，我们提出了一个系统的结构，为每一个选择的类型向量使用部分蔓延和向日葵。对于最小距离较低的标志码，我们调整了之前的结构，并对其表征提供了一些结果，特别是在第三最佳可能距离值的情况下。

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

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.