Narain CFTs and error-correcting codes on finite fields
Shinichiro Yahagi
Abstract
A bstract We construct Narain CFTs from self-dual codes on the finite field F p through even self-dual lattices for any prime p > 2. Using this correspondence, we can relate the spectral gap and the partition function of the CFT to the error correction capability and the extended enumerator polynomial of the code. In particular, we calculate specific spectral gaps of CFTs constructed from codes and compare them with the largest spectral gap among all Narain CFTs.
Topics & Concepts
Finite fieldPrime (order theory)MathematicsDual (grammatical number)Partition function (quantum field theory)Code (set theory)PolynomialPartition (number theory)Function (biology)Field (mathematics)Pure mathematicsPhysicsDiscrete mathematicsCombinatoricsMathematical analysisComputer scienceQuantum mechanicsLiteratureEvolutionary biologySet (abstract data type)Programming languageArtBiologyCoding theory and cryptographyFinite Group Theory ResearchAlgebraic structures and combinatorial models