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引用次数: 0
摘要
在本文中，我们研究了在阶为 p 的有限平面上，心率可被 p 整除的集合的特殊方向数，其中 p 是素数。我们证明不存在这样一个具有两个特殊方向的集合。我们描述了恰好有三个特殊方向的集合的特征，这从反面回答了吉德利的一个问题。此外，我们还介绍了构造最小心数集合的方法，对于 p 的小值，这些集合恰好有四个特殊方向。
In this paper we study the number of special directions of sets of cardinality divisible by p on a finite plane of order p, where p is a prime. We show that there is no such a set with exactly two special directions. We characterise sets with exactly three special directions which answers a question of Ghidelli in negative. Further we introduce methods to construct sets of minimal cardinality that have exactly four special directions for small values of p.
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.
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