Classical codes and chiral CFTs at higher genus

A bstract Higher genus modular invariance of two-dimensional conformal field theories (CFTs) is a largely unexplored area. In this paper, we derive explicit expressions for the higher partition functions specific class CFTs: code CFTs, which are constructed using classical error-correcting codes. setting, Sp(2 g, ℤ) transformations g Riemann surfaces can be recast as simple set linear maps acting on 2 polynomial variables, comprise an object called enumerator polynomial. The CFT function directly related to polynomial, meaning that solutions constraints from immediately give seemingly consistent at given genus. We then find constraints, plus consistency under degeneration limits surface, greatly reduces number possible CFTs. This work provides step towards full understanding 2d