Cyclic codes are special type of linear block codes such that any cyclic shift of a code-word results in another code-word, and this property is called the cyclic property. Cyclic codes are easier to manipulate considering other linear block codes, and they are more preferred in practical communication systems considering the other linear block codes. Polynomials can be utilized for the characterization of cyclic codes, and this enables the cyclic codes to be analyzed analytically, and they can be constructed in an algebraic manner. For the design of a cyclic code, it is essential to determine the generator polynomial of the cyclic code. In this chapter, we will explain the construction of cyclic codes along with their encoding and decoding operations. For this purpose, we give information about determination of the generator polynomials of the cyclic codes and explain the systematic and non-systematic encoding of cyclic codes. In sequel, matrix representations of the generator and parity check polynomials of the cyclic codes are described.
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