Linear block codes

Abstract

The article discusses systematic cyclic linear block codes. A block code uses an encoder that accepts a block of message symbols, and generates a block of code word symbols at the output. This type is in contrast to a convolutional code when the encoder accepts a continuous stream of symbols and similarly generates a continuous encoded output stream. A code is linear if the addition of any two valid code words results in another valid code word. Similarly, a code is cyclic if a circular shift of any valid code word results in another valid code word. The term systematic is used for codes in which the code word contains the message symbols in an unaltered form. Systematic code words are formed by appending additional symbols to the message. These additional symbols are called redundancy or parity symbols. The term symbols as used in this article denotes the individual elements of a code word. In a binary code, the symbols are bits and in a non-binary code, the symbols are collections of bits (e.g., bytes).