General Structure and Properties of Cyclic Codes Over \(GF_2\)
Beatrice Gacheri Munjuri *
Department of Mathematics, Meru University of Science and Technology, Kenya.
Loyford Njagi
Department of Mathematics, Meru University of Science and Technology, Kenya.
Josphine Mutembei
Department of Mathematics, Meru University of Science and Technology, Kenya.
*Author to whom correspondence should be addressed.
Abstract
This article provides a comprehensive analysis of cyclic codes in GF(2), focusing on their general structure and key properties. Cyclic codes are characterized by their generator polynomials, which define their structure and play a crucial role in encoding and decoding processes. The cyclical shift property, inherent in cyclic codes, facilitates efficient implementation using shift register circuits, making them practical for real-world applications. The discussion highlights the algebraic properties that distinguish cyclic codes from other linear block codes, emphasizing their ability to detect and correct errors.
Keywords: Cyclic codes, algebraic properties, generator function