Additive rank-one nonincreasing maps on Hermitian matrices over the field GF(4)

Abstract

A complete classification of additive rank–one nonincreasing maps on hermitian matrices over Galois field GF(2²) is obtained. This field is special and was not covered in a previous
paper. As a consequence, some known applications, like the classification of additive rank–additivity preserving maps, are extended to arbitrary fields. An application concerning the preservers of hermitian varieties is also presented.