This paper introduces some basic principles for extending the classical systolic synthesis methodology to multi-dimensional time. Multi-dimensional scheduling enables complex algorithms that do not admit linear schedules to be parallelized, but it also requires the use of memories in the architecture. We explain how to obtain compatible allocation and memory functions for vlsi (or simd-like code) generation. We also present an original mechanism for controlling a vlsi architecture that has a multi-dimensional schedule. A structural vhdl code has been derived and synthesized (for implementation on fpga platforms) using these systematic design principles. These results are preliminary steps to the hardware synthesis for multi-dimensional time.