Codes over GF(4) and F~2 x F~2 and Hermitian lattices over imaginary quadratic fields
Kok Seng Chua · Proceedings of the American Mathematical Society · 2005
We introduce a family of bi-dimensional theta functions which give uniformly explicit formulae for the theta series of hermitian lattices over imaginary quadratic fields constructed from codes over GF(4) and F 2 x F 2 , and give an interesting geometric characterization of the theta series that arise in terms of the basic strongly modular lattice Z + √Z. We identify some of the hermitian lattices constructed and observe an interesting pair of non-isomorphic 3/2 dimensional codes over F 2 × F 2 that give rise to isomorphic hermitian lattices when constructed at the lowest level 7 but nonisomorphic lattices at higher levels. The results show that the two alphabets GF(4) and F 2 x F 2 are complementary and raise the natural question as to whether there are other such complementary alphabets for codes.