Optimal subcodes of second order Reed-Muller codes and maximal linear spaces of bivectors of maximal rank

Authors
Maks, J Simonis, J
Citation
J. Maks et J. Simonis, Optimal subcodes of second order Reed-Muller codes and maximal linear spaces of bivectors of maximal rank, DES CODES C, 21(1-3), 2000, pp. 165-180
Citations number
26
Categorie Soggetti
Computer Science & Engineering
Journal title
DESIGNS CODES AND CRYPTOGRAPHY
ISSN journal
09251022 → ACNP
Volume
21
Issue
1-3
Year of publication
2000
Pages
165 - 180
Database
ISI
SICI code
0925-1022(200010)21:1-3<165:OSOSOR>2.0.ZU;2-O
Abstract
There are exactly two non-equivalent [32, 11, 12]-codes in the binary Reed- Muller code RM(2, 5) which contain RM(1, 5) and have the weight set {0, 12, 16, 20, 32}. Alternatively, the 4-spaces in the projective space P(Lambda F-2(2)5) over the vector space Lambda F-2(2)5 for which all points have ran k 4 fall into exactly two orbits under the natural action of PGL(5) on P(La mbda F-2(2)5).