Korean J. Math.  Vol 26, No 3 (2018)  pp.537-544
DOI: https://doi.org/10.11568/kjm.2018.26.3.537

The $q$-adic liftings of codes over finite fields

Young Ho Park

Abstract


There is a standard construction of lifting cyclic codes over the prime finite field $\mathbb{Z}_p$ to the rings $\mathbb{Z}_{p^e}$ and to the ring of $p$-adic integers. We generalize this construction for arbitrary finite fields. This will naturally enable us to lift codes over finite fields $\mathbb{F}_{p^r}$ to codes over Galois rings $GR(p^e,r)$. We give concrete examples with all of the lifts.

Keywords


codes over rings, lifting, p-adic codes, Galois rings

Subject classification

94B05, 11T71

Sponsor(s)

This work was supported by 2016 Research Grant from Kangwon National Uni- versity (No. 520160208).

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