Binary Extended Perfect Codes of Length 16 by the Generalized Concatenated Construction
Problems of Information Transmission
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
The Steiner quadruple systems of order 16
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
On resolvability of Steiner systems S(v = 2m, 4, 3) of rank r ≤ v - m + 1 over $$\mathbb{F}_2 $$
Problems of Information Transmission
Discrete Applied Mathematics
On one transformation of Steiner quadruple systems S(υ, 4, 3)
Problems of Information Transmission
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A Steiner quadruple system SQS(v) of order v is a 3-design T (v, 4, 3, 驴) with 驴 = 1. In this paper we describe all nonisomorphic systems SQS(16) that can be obtained by the generalized concatenated construction (GC-construction). These Steiner systems have rank at most 13 over $$ \mathbb{F} $$ 2. In particular, there is one system SQS(16) of rank 11 (points and planes of the a fine geometry AG(4, 2)), fifteen systems of rank 12, and 4131 systems of rank 13. All these Steiner systems are resolvable.