Code generator and decoder based on multiple fields for communication systems

A method of encoding data for transmission from a source (101, 105) to a destination (170) by a communications channel (145), the method comprising: obtaining an ordered set of input symbols representing data to be encoded; selecting a plurality of formations of field values ​​in each field formation is a formation of finite field and the plurality of field formations include at least two different formations finite field; the method characterized by generating a data structure representing a coefficient matrix with entries from being at least two of the plurality of field formations, which formations are different finite field; generating output symbols as linear combinations of input symbols with coefficients taken from the data structure representing the coefficient matrix; and use the generated output symbols and coding for data for transmission from source to destination.