A routing multiplexer system provides p outputs based on a selected permutation of p inputs. Each of a plurality of modules has two inputs, two outputs and a control input and is arranged to supply signals at the two inputs to the two outputs in a direct or transposed order based on a value of a bit at the control input. A first p/2 group of the modules are coupled to the n inputs and a second p/2 group of the modules provide the n outputs. A plurality of control bit tables each contains a plurality of bits in an arrangement based on a respective permutation. The memory is responsive to a selected permutation to supply bits to the respective modules based on respective bit values of a respective control bit table, thereby establishing a selected and programmable permutation of the inputs to the outputs.