Delsarte–Goethals code

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

History

The concept was introduced by mathematicians Philippe 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 for even m ≥ 4 and 0 ≤ r ≤ m/2 − 1 is a binary, non-linear code of length, size and minimum distance
The code sits between the Kerdock code and the second-order Reed–Muller codes. More precisely, we have
When r = 0, we have DG = K and when r = m/2 − 1 we have DG = RM.
For r = m/2 − 1 the Delsarte–Goethals code has strength 7 and is therefore an orthogonal array OA(.