Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Mathematics
Codes Over Rings From Curves Of Higher Genus, José Felipe Voloch, Judy L. Walker
Codes Over Rings From Curves Of Higher Genus, José Felipe Voloch, Judy L. Walker
Department of Mathematics: Faculty Publications
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 …