The code over a finite field F, of a design D is the space spanned by the incidence vectors of the blocks. It is shown here that if D is a Steiner triple system on v points, and if the integer then the ternary code C of contains a subcode that can be shortened to the ternary generalized Reed-Muller
On the binary codes of Steiner triple systems
โ Scribed by Alphonse Baartmans, Ivan Landjev, Vladimir D. Tonchev
- Book ID
- 118771453
- Publisher
- Springer
- Year
- 1996
- Tongue
- English
- Weight
- 661 KB
- Volume
- 8
- Category
- Article
- ISSN
- 0925-1022
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
The binary linear codes generated by incidence matrices of the 80 Steiner triple systems on 15 points (STS( )) are studied. The 80 codes of length 35 spanned by incidence vectors of the points are all non-isomorphic. In contrast, a pair of codes of length 15 generated by blocks are isomorphic if and
1 he existence of reverse Steiner triple systems It.e. Steiner triple systems with a given involutory automorphism of speck4 type) is investigated. it is srfrwrn that such a system exists far alI wders n if n z t of 3 or 9 (mod 24: except posd&ly far n = 25. A system with this grspetty exists also f