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No, if you assume that the size of each object is constant, O notation will swallow it and report that, in terms of the number of items to sort, Radix sort is linear in time.

The usual bound of Omega(n log n), proved using decision trees, is only applicable when your only operation is to compare two elements. Radix sort asks for more than this, and so it can assume a specific structure of its input, so it can violate the lower bound.

Depending on which operations you assume, sorting can become more or less easy. In the extreme case, if you can ask the array "Please sort yourself." as a basic operation, sorting is O(1). Radix sort assumes bitmasking as a basic operation, which falls into the "make things easier" spectrum, leading to an O(n) algorithm under the stated assumption of constant bit length (or any encoding, really, it doesn't really need to be bits).

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