## (Dual) Plotkin Bound for *n* = 2

It follows immediately from the (dual) Plotkin bound that an orthogonal array OA(*b*^{k+t}, *k* + *t* + *n*, *S*_{b}, *k*) or a linear [*k* + *t* + *n*, *n*, *k* + 1]-code can only exist if

*t*≥ (

*k*+ 1)−

*n*+ 1.

For *n* = 2 this yields

*t*≥ (

*k*+ 1) − 1 = (

*k*+ 1)/

*b*−1,

showing that if *k* turns towards infinity, *t* must also turn towards infinity.

Thus, an OA(*b*^{k+t}, *k* + *t* + 2, *S*_{b}, *k*) and a linear [*k* + *t* + 2, 2, *k* + 1]-code with fixed finite *t* cannot exist for arbitrarily large *k*.

### Copyright

Copyright © 2004, 2005, 2006, 2007, 2008, 2009, 2010 by Rudolf Schürer and Wolfgang Ch. Schmid.

Cite this as: Rudolf Schürer and Wolfgang Ch. Schmid. “(Dual) Plotkin Bound for *n* = 2.”
From MinT—the database of optimal net, code, OA, and OOA parameters.
Version: 2008-04-04.
http://mint.sbg.ac.at/desc_CBoundPlotkinInf.html