Phase and amplitude modulation of single or multiple pulses and/or dual polarizations are used in a digital communications system which transmits multidimensional codes. Four dimensional code transmission is specifically disclosed, although the scheme may be extended to eight-dimensional and even 16-dimensional code transmission. The four-dimensional codes are constructed by mapping a digital word into two two-dimensional plane as two sets of x and y coordinates. Signals proportional to these x and y coordinates are used to modulate a transmitted pulse or pulses. When a single pulse is used to transmit the four-dimensional code, polarization modulation is used. A signal proportional to the square root of the sum of the squares of the coordinates assigned to both the horizontal and vertical polarizations is used to control the total RF amplitude of the pulse. A signal proportional to the ratio of the square roots of the sum of the squares to each set of coordinates is used to control the ratio of horizontal to vertical polarization. Finally, the phases of the two polarizations are controlled by signals proportional to the ratios of the coordinates in the respective sets of coordinates. When two pulses are used to transmit the four-dimensional code, quadrature amplitude modulation is used. Signals proportional to the coordinates of each set are used to quadrature amplitude modulate a respective one of the two pulses. Encoding and decoding between digital and the four-dimensional code is accomplished with read only memories.