On Some Designs and Codes from Primitive Representations of Some Finite Simple Groups

Abstract

We examine a query posed as a conjecture by Key and Moori [11, Section 7] concerning the full automorphism groups of designs and codes arising from primitive permutation representations of finite simple groups, and based on results for the Janko groups $J_1$ and $J_2$ as studied in [11]. Here, following that same method of construction, we show that counter-examples to the conjecture exist amongst some representations of some alternating groups, and that the simple symplectic groups in their natural representation provide an infinite class of counter-examples.