ABSTRACT
Algebraic coding theory is the science of detecting and correcting errors on noisy information channels via algebraic techniques. One of the main goals of coding theory is to discover codes with large code rate and large Hamming distance. The decoding scheme is called syndrome decoding, because it offers the symptoms of the errors. The chapter outlines elements of Hamming code and its definition, some important properties, and a decoding algorithm for the code. A convolutional coding scheme has memory, it is convenient to describe it in terms of polynomials. A good convolutional coding scheme should overcome the two types of error propagation. These are: ordinary error propagation and catastrophic error propagation. The encoding operation implemented via shift-registers can be described by a state diagram. The chapter summarizes the parameters for the specification of the binary Bose-Chaudhuri-Hocquenghem (BCH) codes. It provides guidelines and examples to elucidate important steps in the design of binary BCH codes.
