• Korean Journal of Mathematics
• /
• v.13 no.1
• /
• pp.103-112
• /
• 2005

Using the Newton's identities, we give the inductive formula for the generator polynomials of the $p$-adic quadratic residue codes.

• Korean Journal of Mathematics
• /
• v.26 no.3
• /
• pp.537-544
• /
• 2018

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.

• Korean Journal of Mathematics
• /
• v.23 no.1
• /
• pp.163-169
• /
• 2015

We give idempotent generators for quadratic residue codes over p-adic integers and over the rings $\mathbb{Z}_{p^e}$.