对称和子空间 2 设计的可加性

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

Designs, Codes and Cryptography Pub Date : 2024-07-05 DOI:10.1007/s10623-024-01452-4

Marco Buratti, Anamari Nakić

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引用次数: 0

摘要

如果可以将一个 2-（(v,k,\lambda )\）设计嵌入到一个合适的无方群 G 中，使得其块集包含在（或重合于）其点集的所有零和 k 子集的集合中，那么这个设计就是可加的（或强可加的）。本文给出了对称设计和子空间 2 设计的可加性或强可加性的明确结果。特别是，PG（_d(n,q)\）的强可加性总是成立的，而已知的可加性只适用于\(q=2\)或\(d=n-1\)。

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Additivity of symmetric and subspace 2-designs

A 2-\((v,k,\lambda )\) design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group G in such a way that its block set is contained in (or coincides with) the set of all zero-sum k-subsets of its point set. Explicit results on the additivity or strong additivity of symmetric designs and subspace 2-designs are presented. In particular, the strong additivity of PG\(_d(n,q)\), which was known to be additive only for \(q=2\) or \(d=n-1\), is always established.

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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.