Abstract
Abstract Coding theory is an application of algebra that has become increasingly important over the last several decades. Probability, combinatorics, group theory, linear algebra, and polynomial rings over finite fields all play important roles in coding theory. The paper contains an investigation on coding and error Detection, Error correction. A brief introduction to basic algebraic concepts is given. Error detection, Correction and Decoding are discussed. Linear codes generator matrices and parity-check are introduced. Perfect and Hamming codes are considered. Several examples are given.