On the ratio between the maximal T-complexity and the T-complexity of random strings

This paper derives an asymptotic closed form expression for the ratio between minimal codeword length in systematic T-augmentation and expected codeword length in random T-augmentation, confirming existing empirical results by Hamano. We also show that this ratio corresponds, in the limit, to the ratio between the maximal T-complexity and the T-complexity of random strings of a given string length.