The Existence of Minimal Logarithmic Signatures for Some Finite Simple Groups

Abstract

The M LS conjecture states that every finite simple group has a minimal logarithmic signature. The aim of this paper is proving the existence of a minimal logarithmic signature for some simple unitary groups P SU n (q). We report a gap in the proof of the main result of [H. Hong, L. Wang, Y. Yang, Minimal logarithmic signatures for the unitary group U n (q), Des. Codes Cryptogr. 77 (1) (2015) [179][180][181][182][183][184][185][186][187][188][189][190][191] and present a new proof in some special cases of this result. As a consequence, the M LS conjecture is still open.

Homomorphic Stability of Finite Groups

“…Such factorizations are called a minimal logarithmic signature (MLS). It is known that the existence of MLS for any finite group can be reduced to the existence of MLS for finite simple groups [5].…”