# Delsarte–Goethals code

From BitcoinWiki

This is the approved revision of this page, as well as being the most recent.

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

## Contents

## History[edit]

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[edit]

The Delsarte–Goethals code DG(*m*,*r*) 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(*m*,*r*) = *K*(*m*) and when *r* = *m*/2 − 1 we have DG(*m*,*r*) = RM(2,*m*).

For *r* = *m*/2 − 1 the Delsarte–Goethals code has strength 7 and is therefore an orthogonal array OA(.

## Source[edit]

## See Also on BitcoinWiki[edit]