Cyclic codes over the ring of 4-adic integers of lengths 15, 17 and 19

초록

We present a new way of obtaining the complete factorization of $X^n-1$ for $n=15,17,19$ over the $4$-adic ring ${\text{O}}_4[X]$ 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.

키워드