Korean J. Math.  Vol 27, No 3 (2019)  pp.767-777
DOI: https://doi.org/10.11568/kjm.2019.27.3.767

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

Young Ho Park

Abstract


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.

Keywords


Cyclic codes, Galois rings, $q$-adic codes, Lifting

Subject classification

94B05

Sponsor(s)

This work was supported by 2017 Research Grant from Kangwon National University (No.\,520170501)

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