ABSTRACT
The main method for constructing good binary codes is to start from good linear codes over an extension field FQ and to go down from FQ to F2 using concatenation, subfield codes or the trace. The largest and most useful family of binary linear codes which we encountered in this text, the cyclic codes, are constructed in this fashion. Codes with small distance have a long history in computer memory systems. An interesting situation arises when a multiple-bit-per-chip organization is used. In this case the bits are grouped together in bytes, where each byte has m bits.
