Author:
Tonchev Vladimir,Wassermann Alfred
Abstract
AbstractThe classification of unitals with parameters 2-(28, 4, 1) according to the 2-rank of their incidence matrices was initiated by McGuire, Tonchev and Ward, who proved that the 2-rank of any unital on 28 points is greater than or equal to 19, and up to isomorphism, there is a unique unital with 2-rank equal to 19. Jaffe and Tonchev investigated the next two 2-ranks, 20 and 21, and showed that there are no unitals on 28 points with 2-rank equal to 20, and there are exactly 4 isomorphism classes of unitals of rank 21. The subject of this paper is the classification of unitals having 2-rank 22, 23 and 24.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory
Reference29 articles.
1. Al-Azemi, A., Betten, A., Betten, D.: Unital designs with blocking sets. Discrete Appl. Math. 163, 102–112 (2014). https://doi.org/10.1016/j.dam.2013.02.023(Optimal Discrete Structures and Algorithms ODSA 2010)
2. Beth, T., Jungnickel, D., Lenz, H.: Design Theory, vol. 1, 2nd edn. Cambridge University Press, Cambridge (1999)
3. Betten, A., Betten, D., Tonchev, V.D.: Unitals and codes. Discrete Math. 267(1–3), 23–33 (2003). https://doi.org/10.1016/S0012-365X(02)00600-3
4. Betten, A., Braun, M., Fripertinger, H., Kerber, A., Kohnert, A., Wassermann, A.: Error-Correcting Linear Codes: Classification by Isometry and Applications (Algorithms and Computation in Mathematics), 1st edn. Springer, Berlin (2006)
5. Bouyukliev, I., Bouyuklieva, S., Kurz, S.: Computer classification of linear codes. IEEE Trans. Inf. Theory 1, 1 (2021). https://doi.org/10.1109/TIT.2021.3114280
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Unitals in Projective Planes of Order 25;Mathematics in Computer Science;2023-03