Back to Search
Start Over
Mutually disjoint Steiner systems from BCH codes.
- Source :
- Designs, Codes & Cryptography; Apr2024, Vol. 92 Issue 4, p885-907, 23p
- Publication Year :
- 2024
-
Abstract
- Liu et al. (IEEE Trans Inf Theory 68:3096–3107, 2022) investigated a class of BCH codes C (q , q + 1 , δ , 1) with q = δ m a prime power and proved that the set B δ + 1 of supports of the minimum weight codewords supports a Steiner system S (3 , δ + 1 , q + 1) . In this paper, we give an equivalent formulation of B δ + 1 in terms of elementary symmetric polynomials and then construct a number of mutually disjoint Steiner systems S (3 , δ + 1 , δ m + 1) when m is even and a number of mutually disjoint G-designs G ( δ m + 1 δ + 1 , δ + 1 , δ + 1 , 3) when m is odd. In particular, the existence of three mutually disjoint Steiner systems S (3 , 5 , 4 m + 1) or three mutually disjoint G-designs G ( 4 m + 1 5 , 5 , 5 , 3) is established. [ABSTRACT FROM AUTHOR]
- Subjects :
- STEINER systems
POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 09251022
- Volume :
- 92
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- Designs, Codes & Cryptography
- Publication Type :
- Academic Journal
- Accession number :
- 176627807
- Full Text :
- https://doi.org/10.1007/s10623-023-01319-0