Constructions of pseudorandom binary lattices

Three constructions for binary lattices with strong pseudorandom properties are given. These constructions are the two dimensional extensions and modifications of three of the most important one dimensional constructions. The upper estimates for the pseudorandom measures of the binary lattices constructed are based on the principle that character sums in two variables can be estimated by fixing one of the variables, then we get a character sum in one variable which can be estimated by using Weil's theorem.