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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(''m'',''r'') for even ''m'' ≥ 4 and 0 ≤ ''r'' ≤ ''m''/2 − 1 is a binary, [[non-linear code]] of length <math>2^{m}</math>, size <math>2^{r(m-1)+2m}</math> and [[Block code#The distance d|minimum distance]] <math>2^{m-1} - 2^{m/2-1+r}</math>

The code sits between the [[Kerdock code]] and the second-order [[Reed–Muller code]]s. More precisely, we have

: <math>K(m) \subseteq DG(m,r) \subseteq RM(2,m)</math>

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(<math>2^{3m-1}, 2^m, \mathbb{Z}_2, 7)</math>.

==Source==

[http://wikipedia.org/ http://wikipedia.org/]

[[Category:Error-correcting codes]]
==See Also on BitcoinWiki==
* [[Bitacium]]
* [[FAST INVEST]]
* [[DeepToken]]
* [[CryptoAds]]
* [[International Science Hub]]

Delsarte–Goethals code - Revision history

Admin: Created page with "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 thei..."