Written out
Every accidental is written in, rather than left to a key signature, so the letters can be read one at a time.
The step pattern
A♯WB♯WC𝄪WD𝄪HE♯WF𝄪WG𝄪HA♯
What is true of it
A♯ Lydian is A♯, B♯, C𝄪, D𝄪, E♯, F𝄪 and G𝄪, and back to A♯.
Its steps are W – W – W – H – W – W – H, where W is a whole step and H a half.
Written correctly it needs 11 alterations, C𝄪, D𝄪, F𝄪 and G𝄪 among them. That is what the letters force, and it is also why nobody writes music in this key: the same notes spelled from the other side are easier to read.
On the same tonic, A♯ major differs from it by exactly one note.
Across the first twelve frets of the ukulele its notes fall in 32 places, which is what makes a scale a shape rather than a list.
Chords made only of these notes
Found by testing every chord in the catalogue against these 7 sounds, not chosen.