Binary codes with large symbols

Abstract

Maximum distance separable (MDS) codes which are defined over larger alphabets require that 1) the encoding and decoding procedures are performed as operations over a finite field, and 2) an update in a single information bit requires an update in the redundancy symbols and usually affects a number of bits in each redundancy symbol. Thus, the optimal redundancy is achieved at the expense of additional complexity in the encoding/decoding procedures as well as the number of redundancy bits affected by an update in the information.