Directed Circulant graphs and Binary Cyclic codes

**ABSTRACT:**

Various papers have been written on the theory of circulant graphs3,6,8,9,10. Also graphs with circulant adjacency matrices is discussed in7. Circulant graphs have important applications to the theory of designs and error correcting codes12. This paper is a study of relationship between circulant graphs and binary linear codes. It establishes a strong connection between directed circulant graphs and binary cyclic codes . Each binary cyclic code corresponds to an equivalence class of directed circulant graphs. Circulant graphs associated with combination of cyclic codes is also discussed.

**KEYWORDS: **Cayley graphs, circulant graphs, adjacency matrix, cyclic codes, generator polynomial, generator matrix.

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Various papers have been written on the theory of circulant graphs3,6,8,9,10. Also graphs with circulant adjacency matrices is discussed in7. Circulant graphs have important applications to the theory of designs and error...