CYCLIC CODES OVER THE RING OF 4-ADIC INTEGERS OF LENGTHS 15, 17 AND 19

We present a new way of obtaining the complete factorization of $X^n-1$ for n = 15, 17, 19 over the 4-adic ring ${\mathcal{O}}_4[X]$ of integers and thus over the Galois rings $GR(2^e,2)$. As a result, we determine all cyclic codes of lengths 15, 17 and 19 over those rings. This extends our previous work on such cyclic codes of odd lengths less than 15.