On the support t-designs of extremal Type III and IV codes

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2022-07-20 DOI:10.1007/s00200-022-00571-6

Tsuyoshi Miezaki, Hiroyuki Nakasora

引用次数: 0

Abstract

Let C be an extremal Type III or IV code and \(D_{w}\) be the support design of C for weight w. We introduce the numbers, \(\delta (C)\) and s(C), as follows: \(\delta (C)\) is the largest integer t such that, for all weights, \(D_{w}\) is a t-design; s(C) denotes the largest integer t such that w exists and \(D_{w}\) is a t-design. Herein, we consider the possible values of \(\delta (C)\) and s(C).

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关于极值III和IV型码的支持t-设计

让 C 是极值类型 III 或 IV 码，\(D_{w}\) 是 C 对于权重 w 的支持设计。我们引入数字 \(\delta (C)\) 和 s(C) 如下：\(\delta(C)\)是指对于所有权重，\(D_{w}\)是一个t设计的最大整数t；s(C)表示w存在且\(D_{w}\)是一个t设计的最大整数t。在这里，我们考虑了 \(\delta (C)\) 和 s(C) 的可能值。

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

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.