A method for constructing rotated Z^n-lattices, with n a power of 2, based on totally real subfields of the cyclotomic field Q(\zeta_{2^r}), where r\geq 4 is an integer, is presented. Lattices exhibiting full diversity in some dimensions n not previously addressed are obtained.

In this paper we generalize the ball-collision algorithm by Bernstein, Lange, Peters from the binary field to a general finite field. We also provide a complexity analysis and compare the asymptotic complexity to other generalized information set decoding algorithms.