Binary Cyclic Codes in Circular Cliques

Abstract

In this paper, we study the relationship between circular cliques and binary cyclic codes. We introduced the concept of binary cyclic codes in circular cliques. Every circular clique Kk/d clearly admits a (k,d)- vertices. We observed that a circular clique Kk/d with gcd(k, d) = 1 if d ? |i? j| ? k?d are Prime circular cliques.

Introduction

Conclusion

In this paper, we introduced the concept of binary cyclic codes in circular cliques. The circular cliques and a binary cyclic codes are presented and proved. Every circular clique Kk/d clearly admits a (k,d)- vertices. We observed that a circular clique Kk/d with gcd(k, d) = 1 are Prime circular cliques. The degree of the generating polynomials are decreased. 1) 1.K7/1, K7/2 , K7/3……( k=0…..n-1 vertices) gcd (k(x), x7 – 1) = x+1. Hence X corresponds to the cyclic code C = , the degree of the generator polynomial k(x) are 3,2 and 1, dimension of the code is 6 and has no error correcting codes. 2) K11/1, K11/2 , K11/3……( k=0…..n-1 vertices) gcd (k(x), x11 – 1) = x+1. Hence X corresponds to the cyclic code C = , the degree of the generator polynomial k(x) is 1, dimension of the code is 10 and has no error correcting codes. We now seek a condition under which the cyclic code corresponding to one circular cliques becomes a subset of another.

References

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Copyright

Copyright © 2024 Dr. D. Bharathi, K. Ranga Devi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.