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Hi,

How are they different?

Sorry for giving you short notice

Sorry for giving you a short notice.

Sorry for giving you such a short notice.

Sorry for giving you such short notice.
Comments 
To me, only the third sentence is correct.
HI,

#1 is also fine.

'Notice' is normally treated as non-countable in such a context.

Best wishes, Clive
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I would go for #4 over #3.
giving you short notice or giving you such short notice is correct, in this meaning is "notice" uncountable - Oxford Collocations Dictionary
Hi,

Both phrases are correct, with different meanings.

uncountable.

Clive
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