The Existence of Minimal Logarithmic Signatures for Some Finite Simple Unitary Groups

The MLS 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 S U n ( q ). We report a gap in the proof of the main result of Hong et al. (Des. Codes Cryptogr. 77: 179–191, 2015 ) and present a new proof in some special cases of this result. As a consequence, the MLS conjecture is still open.

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