Reduction for block-transitive t- $$(k^2,k,\lambda )$$ designs

IF 1.4 2区数学 Q3 COMPUTER SCIENCE, THEORY & METHODS Designs, Codes and Cryptography Pub Date : 2024-08-09 DOI:10.1007/s10623-024-01477-9

Haiyan Guan, Shenglin Zhou

引用次数: 0

Abstract

In this paper, we study block-transitive automorphism groups of t-$(k^2,k,\lambda )$ designs. We prove that a block-transitive automorphism group G of a t-$(k^2,k,\lambda )$ design must be point-primitive, and G is either an affine group or an almost simple group. Moreover, the nontrivial t-$(k^2,k,\lambda )$ designs admitting block-transitive automorphism groups of almost simple type with sporadic socle and alternating socle are classified.

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块传递 t- $$(k^2,k,\lambda )$$ 设计的还原

在本文中，我们研究了 t-\((k^2,k,\lambda )\ 设计的块变换自变群。我们证明了 t-\((k^2,k,\lambda )\ 设计的块变换自变群 G 必须是点原始的，并且 G 要么是仿射群，要么是近似简单群。此外，我们还对容许具有零星社会群和交替社会群的几乎简单类型的块传递自变群的非难t-\((k^2,k,\lambda )\设计进行了分类。

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.