On Codes from Norm-Trace Curves

The main results of this paper are derived by using only simple Gröbner basis techniques. We present a new construction of evaluation codes from MiuraKamiya curves Cab. We estimate the minimum distance of the codes and estimate the minimum distance of a class of related one-point geometric Goppa codes. With respect to these estimates the new codes perform at least as well as the related geometric Goppa codes. In particular we consider codes from norm-trace curves. We show that our estimates give actually the true minimum distance of these codes. The new codes from norm-trace curves perform rather well. In many cases much better than the corresponding geometric Goppa codes. It turns out that an alternative description of the new codes from norm-trace curves can be made by using Høholdt et al.’s construction of improved dual codes ([11]).