caa a22 4500 477040845 CHVBK 20180405111317.0 cr unu---uuuuu 170330e19961001xx s 000 0 eng 10.1023/A:1027337923268 doi (NATIONALLICENCE)springer-10.1023/A:1027337923268 Carpenter Laurel Clemson University, 29634, Clemson, SC aut Oval Designs in Desarguesian Projective Planes [Elektronische Daten] [Laurel Carpenter] Given any projective plane Π of even order qcontaining a hyperoval $${\mathcal{O}}$$ , a Steiner 2- $$2 - (\left( {_2^q } \right),\tfrac{q}{2},1)$$ design can be constructed. The 2-rank of this design is boundedabove by rank2(Π}-q-1. Using a result ofBlokhuis and Moorhouse bm94, we show that this bound is met whenΠ is desarguesian and $${\mathcal{O}}$$ is regular.We also show that the block graph of the Steiner 2-design inthis case produces a Hadamard design which is such that the binarycode of the associated 3-design contains a copy of the first-orderReed-Muller code of length 2 2m , whereq=2m. Kluwer Academic Publishers, 1996 hyperoval nationallicence Hadamard nationallicence oval design nationallicence Reed-Muller nationallicence Designs, Codes and Cryptography Kluwer Academic Publishers 9/1(1996-10-01), 51-59 0925-1022 9:1<51 1996 9 10623 https://doi.org/10.1023/A:1027337923268 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1027337923268 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Carpenter Laurel Clemson University, 29634, Clemson, SC aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 9/1(1996-10-01), 51-59 0925-1022 9:1<51 1996 9 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence SWISSBIB 477040802 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer