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Re:A maximally-dense encoding for n-choose-k (2013) by Someone on Friday May 20, 2022 @10:42AM (#31448117)
If you have to decode n+4, you know the result can’t be in S, as its elements are mapped to {1,…,n}.

So, the result is in T. You subtract n, leaving 4, and use whatever bijection you had for T to decode that into an element of T.

If, on the other hand, you had n-4, you know it must decode to an element of S, and directly use its decoder to find that element.

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