Arbitrary OA / Dual of Arbitrary Code (with Infinite s)

A linear orthogonal array OA(b^m, s, S_b, k) with strength k = 0 exists for all m and all s ≥ m. Its dual is a linear [s, s−m, 1]-code over F_q.

The OA (Arbitrary OA)

Every OA(b^m, s, S_b, k) has strength k = 0. It can be generated by any m×s-matrix over F_b with full rank, e.g. by the first m rows of the s×s-identity matrix.

Its Dual Code (Arbitrary Code)

Every non-singular n×s-matrix over F_b defines an [s, n, 1]-code over F_b.

See Also

• Generalization for arbitrary OOAs

• Corresponding result for nets

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. “Arbitrary OA / Dual of Arbitrary Code (with Infinite s).” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_CK0-inf.html