An alternative construction of the Hermitian unital 2‐(28,  4,  1) design. Issue 12 (26th September 2022)

• Record Type: Journal Article
• Authors: Inoue, Koichi
• Is Part Of: Journal of combinatorial designs. Volume 30:Issue 12(2022)
• Page Start: 752
• Page End: 759
• Publication Date: 2022-09-26
• Subjects: extension of design -- Hermitian unital design -- Witt system; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21861
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: In this paper, we give an alternative construction of the Hermitian unital 2‐(28, 4, 1) design in such a way that it is constructed on the isotropic vectors in a unitary geometry of dimension 3 over the field F 4 ${{\mathbb{F}}}_{4}$ . As a corollary, we can construct a unique 3‐(10, 4, 1) design (namely, the Witt system W 10 ${{\boldsymbol{W}}}_{{\bf{10}}}$ ).