  Recently, trace distance measure of coherence has been proposed for
characterizing the coherence of a given quantum state. However, it seems
difficult to estimate the optimal incoherent state for high dimensional states.
An explicit expression for the trace distance measure of coherence for a class
of qudit states is provided. We show that the closest incoherent state to the
class of qudit states is just the diagonal matrix obtained from it by deleting
all off-diagonal elements. It is also shown that the measure of coherence
induced by trace distance can act as a measure of coherence for this class of
qudit states with some restrictions on the strictly incoherent operations.
