Vol. 14, No. 1, 2015

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An elementary description of the Mathieu dual hyperoval and its splitness

Satoshi Yoshiara

Vol. 14 (2015), No. 1, 81–110
Abstract

An elementary new construction of a 3-dimensional dual hyperoval over F4 is given, as well as an explicit analysis of the structure of its automorphism group. This provides a self-contained introduction to the Mathieu simple group M22. The basic properties of as a dimensional dual hyperoval, e.g. splitness, complements, linear systems, quotients and coverings, are derived from this construction.

Keywords
dimensional dual hyperoval (DHO), the Mathieu DHO, Mathieu group M_22, automorphism group, complement, linear system
Mathematical Subject Classification 2010
Primary: 05B25, 05E18, 20B25, 20D08, 51A45, 51E20
Milestones
Received: 6 May 2014
Accepted: 28 September 2014
Authors
Satoshi Yoshiara