The parity polynomial is the remainder after diving by the generator polynomial it is available in the register after n shifts through the n-k stage feedback registers.

If the syndrome is an all zero vector then the received code-word is a valid code. If the syndrome is a non zero vector then the received code has errors.

A cyclic code can be generated using generator polynomial and block codes can be generated using generator matrix.

Linear codes are used in forward error correction. It allows for more efficient encoding and decoding procedures.

The rate of a block code is the ratio between its message length and the block length, R=k/n.

The block length n is the number of elements in the code word.

The cyclic codes are a subclass of linear codes. It is designed using feedback shift registers.

The cyclic shift of a code-word polynomial and encoding involves division of one polynomial by another. Thus this feedback shift register is also called as dividing circuit.

Extended go-lay code is formed by adding overall parity bit with the perfect bit known as the golay code.

Block codes are generated using generator matrix and cyclic codes are generated using generator polynomial.