Sets of One and Higher Dimensional Welti Codes and Complementary Codes

A Welti code is a binary sequence with an impulse-like autocorrelation function. A set of such codes may possess vanishing cross-correlation functions. The elements of Welti codes must be members of a set of at least two orthogonal vectors or subcodes. First, methods for synthesizing sets of one-dimensional Welti codes with vanishing cross-correlation functions, and conditions upon their existence are discussed. Then, construction methods of sets of two and higher dimensional Welti codes are presented. Based on these constructions, further sets of mutually orthogonal complementary codes in one or more dimensions can be derived. The use of such signals relates to various topics such as communication, radar and navigation systems, measuring and identification in one or higher dimensional systems, synchronization and spatial alignment, or coded aperture imaging.