Union of Pairwise Disjoint Baer Subplanes

If b = q² is a square, q²âˆ’q + 1 disjoint Baer subplanes with cardinality q² + q + 1 exist in the projective plane PG(2, b). By taking the union of i such subplanes, a projective [i(q² + q + 1, 3, i(q² + q)−q]-code over F_b is obtained for all i = 1,…, q²âˆ’q + 1.

See Also

• [1, Section 2.4 and 4.2.8]

References

[1]	Andries E. Brouwer. Bounds on the size of linear codes. In Vera S. Pless and W. Cary Huffman, editors, Handbook of Coding Theory, volume 1, pages 295–461. Elsevier Science, 1998.

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. “Union of Pairwise Disjoint Baer Subplanes.” From MinT—the database of optimal net, code, OA, and OOA parameters. Version: 2024-09-05. http://mint.sbg.ac.at/desc_CBaerSubplanes.html