Abstract:
Let n be a positive integer, y
n − 1 cyclotomic polynomial and Zq be a given finite field. In this study we
determined the number of cyclic codes over Z31. First, we partitioned the cyclotomic polynomial y
n − 1 using
cyclotomic cosets 31 mod n and factorized y
n − 1 using case to case basis. Each monic divisor obtained is a
generator polynomial and generate cyclic codes. The results obtained are useful in the field of coding theory
and more especially, in error correcting codes.
