Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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THE q-ADIC LIFTINGS OF CODES OVER FINITE FIELDS

  • Received : 2018.08.06
  • Accepted : 2018.09.12
  • Published : 2018.09.30
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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.

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References

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