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Relation between spectra of Narain CFTs and properties of associated boolean functions - MaRDI portal

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Relation between spectra of Narain CFTs and properties of associated boolean functions

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Publication:6394362

DOI10.1007/JHEP09(2022)146arXiv2203.11643MaRDI QIDQ6394362

Author name not available (Why is that?)

Publication date: 22 March 2022

Abstract: 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.





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