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 Miura–Kamiya 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.ʹs in: V.S. Pless, W.C. Huffman (Eds.), Handbook of Coding Theory, Vol. 1, Elsevier, Amsterdam, 1998, pp. 871–961 (Chapter 10) construction of improved dual codes.