Is there a standard way to do this?
Googling -- "approximate entropy" bits -- uncovers multiple academic papers but I'd like to just find a chunk of pseudocode defining the approximate entropy for a given bit string of arbitrary length.
(In case this is easier said than done and it depends on the application, my application involves 16,320 bits of encrypted data (cyphertext). But encrypted as a puzzle and not meant to be impossible to crack. I thought I'd first check the entropy but couldn't easily find a good definition of such. So it seemed like a question that ought to be on StackOverflow! Ideas for where to begin with de-cyphering 16k random-seeming bits are also welcome...)
See also this related question:
What is the computer science definition of entropy?
I believe the answer is the Kolmogorov Complexity of the string. Not only is this not answerable with a chunk of pseudocode, Kolmogorov complexity is not a computable function!
One thing you can do in practice is compress the bit string with the best available data compression algorithm. The more it compresses the lower the entropy.