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

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Published: Sep 30, 2019
Keywords:
Cyclic codes, Galois rings, $q$-adic codes, Lifting
Mathematics Subject Classification:
94B05

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Young Ho Park
Department of Mathematics Kangwon National University Chun Cheon 24341, Korea

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.


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Supporting Agencies

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

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