A generalization of the binary Preparata code Original Research Article

A classical binary Preparata code image is a nonlinear image-code, where m is odd. It has a linear representation over the ring image [Hammons et al., The image-linearity of Kerdock, Preparata, Goethals and related codes, IEEE Trans. Inform. Theory 40(2) (1994) 301–319]. Here for any image and any m such that image a nonlinear code image over the field image with parameters image, where image, is constructed. If image this set of parameters generalizes that of image. The equality image is established in the following cases: (1) for a series of initial admissible values q and m such that image; (2) for image and any admissible q, and (3) for admissible q and m such that there exists a number image with image and image. We apply the approach of [Nechaev and Kuzmin, Linearly presentable codes, Proceedings of the 1996 IEEE International Symposium Information Theory and Application Victoria, BC, Canada 1996, pp. 31–34] the code P is a Reed–Solomon representation of a linear over the Galois ring image code image dual to a linear code image with parameters near to those of generalized linear Kerdock code over R.