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This paper investigates the conditions for a rational Narain conformal fieldtheory (Narain CFT) to be constructed from an error-correcting code. Byexamining the compactified bosons on a lattice, we identify the presence of achiral algebra. Our analysis demonstrates that when the lattice and the B-fieldfulfill specific requirements, the partition function can be decomposed into afinite sum of irreducible characters. Additionally, the partition function canbe considered a simple current orbifold with discrete torsion, which isdetermined by the lattice and the B-field. We establish that the partitionfunction can be expressed as a polynomial, with the variables substituted bycertain $q$-series. In a specific scenario, this polynomial corresponds to theweight enumerator polynomial of an error-correcting code. Consequently, theinverse of construction A [DS20, ACD22, Yah22] can be successfully executed.

On the Rationality and the Code Structure of a Narain CFT, and the Simple Current Orbifold