Delsarte–Goethals code

The Delsarte–Goethals code is a type of error correcting code.

History

The concept was introduced by mathematicians Ph. Delsarte and J.-M. Goethals in their published paper.

A new proof of the properties of the Delsarte–Goethals code was published in 1970.

Function

The Delsarte–Goethals code DG(u, r) for even u ≥ 4 and 1 ≤ r ≤ u/2 is a binary, non-linear ($2^{u},2^{(u-1)(u/2-r+1)+u+1},2^{m-1}-2^{m-1-d}$)-code [1]. For r = u/2 − 1 it has strength 7 and is therefore an orthogonal array OA($2^{3u-1},2^{u},\mathbb {Z} _{2},7)$.

External links

• https://www.encyclopediaofmath.org/index.php/Delsarte-Goethals_code