The $q$-adic liftings of codes over finite fields
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초록
There is a standard construction of lifting cyclic codes over the prime finite field $\Z_p$ to the rings $\Z_{p^e}$ 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 $\F_{p^r}$ to codes over Galois rings $GR(p^e,r)$. We give concrete examples with all of the lifts.
Abstract
There is a standard construction of lifting cyclic codes over the prime finite field $\Z_p$ to the rings $\Z_{p^e}$ 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 $\F_{p^r}$ to codes over Galois rings $GR(p^e,r)$. We give concrete examples with all of the lifts.
참고문헌 (7)
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