# Coding theory

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 quickly, contain many valid code words and can correct or at least detect many errors. These aims are mutually exclusive however, so different codes are optimal for different applications. 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 code words
• the minimum Hamming distance between two valid code words

Another concern of coding theory is designing codes that help synchronization. A code may be designed so that a phase shift can be easily detected and corrected and that multiple signals can be sent on the same channel.

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