Coding theory deals with the properties of codes and thus with their fitness for a specific application. The aim of coding theory is to find codes which transmit fast, contain many valid code words and can correct or at least detect many errors. These aims are mutually exclusive however, so each application has its own best code. The needed properties of this code mainly depend on the probability of errors happening during transmission.
The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then further researched. It analyzes the following three properties of a code mainly:
- code word length
- total number of valid codewords
- the minimum Hamming distance between two valid codewords