A new construction of lattices from codes over GF(3)

AbstractWe define a pair of constructions of d-dimensional Z-lattices for d = 0 mod 24 from particular length d ternary linear codes, which supplement the construction of d-dimensional Eisenstein lattices (and hence 2d-dimensional Z-lattices) given by an extension of the work of Sloane (1979) and Conway and Sloane (1988). We show that these constructions produce all of the Niemeier lattices in the case of self-dual codes of length 24, suggesting, by analogy with previous work concerning binary codes, relevance to the classification problem of self-dual conformal field theories in physics. In addition, our intermediate results are of relevance to the classification of self-dual ternary codes of length 24