Codes over the p-adic integers
We study codes over the p-adic integers and correct errors in the existing literature. We show that MDS codes exist over the p-adics for all lengths, ranks and p. We show that self-dual codes exist over the 2-adics if and only if the length is a multiple of 8 and that self-dual codes exist over the p-adics with p odd if and only if the length is 0 (mod 4) for p equivalent to 3 (mod 4) and 0 (mod 2) for p equivalent to 1 (mod 4).
codes over the p-adics mds codes self-dual codes