Methods and apparatus for encoding data

In a coded orthogonal frequency division multiplex (COFDM) system n-bit data words are encoded as m-symbol code words (binary, quaternary, octary, etc.). The code words are selected for desired low peak-to-mean envelope power ratio (PMEPR) characteristics of transmissions over a COFDM channel, from a set of cosets of a linear sub-code of a code having a specified generator matrix. The code words thus identified by the procedure described can, even for values of m in excess of 3, simultaneously limit the PMEPR to a known value, provide specified error control characteristics, be implemented in a feasible manner using analytical circuit techniques (e.g. with combinatorial logic), and include sufficiently many different code words to enable data to be transferred at useful rates. In particular, sets of cosets can be identified without calculating the maximum peak envelope power over each coset. Various selections of code words can be made, enabling a reduced error detection capability to be accepted in order to obtain a higher data transfer rate.