Enumeration of Cyclic Codes Over GF(23)

In this paper, we investigate the number of irreducible polynomials of
-1
over GF(23). First, We factorize
-1
into irreducible polynomials over GF(23) using the cyclotomic cosets of 23 modulo
. The number of irreducible polynomial factors of
-1
over GF(23) is equal to the number of cyclotomic cosets of 23 modulo n and each monic divisor of
-1
is a generator polynomial of cyclic codes in GF(23). Succeedingly, we confirm that the number of cyclic codes of length
over
finite field GF(23) is equivalent to the number of polynomials that divide
-1
.

In conclusion, we enumerate the number of cyclic codes of length n for l

< 24 and as
= 23
for l

< 24