A compact and fast coder-decoder of the Reed-Solomon type and a reader, which comprises such a coder-decoder. The present invention provides a coder-decoder that includes specific registers that are divided into elementary cells set in series and comprising means of multiplexing and of calculation such that during a cycle of a clock signal the data of two of the registers are shifted from one cell and a calculation operation is carried out for one of the data and it is subsequently possible to exchange simultaneously the data between the two registers.