  Recently, the construction of Narain CFT from a certain class of quantum
error correcting codes has been discovered. In particular, the spectral gap of
Narain CFT corresponds to the binary distance of the code, not the genuine
Hamming distance. In this paper, we show that the binary distance is identical
to the so-called EPC distance of the boolean function uniquely associated with
the quantum code. Therefore, seeking Narain CFT with high spectral gap is
equivalent to getting a boolean function with high EPC distance. Furthermore,
this problem can be addressed by finding lower Peak-to-Average Power ratio
(PAR) with respect to the binary truth table of the boolean function. Though
this is neither sufficient nor necessary condition for high EPC distance, we
construct some examples of relatively high EPC distances referring to the
constructions for lower PAR. We also see that codes with high distance are
related to induced graphs with low independence numbers.
