Date of this Version
Published in IEEE Transactions on Information Theory, vol 45, iss 6 (Sept 1999), pp 1768-1776 DOI: 10.1109/18.782098
We construct certain error-correcting codes over finite rings and estimate their parameters. These codes are constructed using plane curves and the estimates for their parameters rely on constructing “lifts” of these curves and then estimating the size of certain exponential sums.
THE purpose of this paper is to construct certain error-correcting codes over finite rings and estimate their parameters. For this purpose, we need to develop some tools; notably, an estimate for the dimension of trace codes over rings (generalizing work of van der Vlugt over fields and some results on lifts of affin curves from field of characteristic p to Witt vectors of length two. This work partly generalizes our previous work on elliptic curves, although there are some differences which we will point out below.