An improved product construction of rotational Steiner quadruple systems. (English) Zbl 1012.05020
Summary: An improved product construction is presented for rotational Steiner quadruple systems. Direct constructions are also provided for small orders. It is known that the existence of a rotational Steiner quadruple system of order \(\upsilon +1\) implies the existence of an optimal optical orthogonal code of length \(\upsilon\) with weight four and index two. New infinite families of orders are also obtained for both rotational Steiner quadruple systems and optimal optical orthogonal codes.
MSC:
| 05B05 | Combinatorial aspects of block designs |
References:
| [1] | Bitan, Designs Codes and Crypt 3 pp 283– (1993) |
| [2] | Introduction to the Theory of Groups of Finite Order, Ginn, Boston, 1937; reprinted by Dover, New York, 1956. |
| [3] | Colbourn, London Math Soc Lecture Note Ser 267 pp 37– (1999) |
| [4] | Chung, IEEE Trans Inform Theory 35 pp 595– (1989) |
| [5] | Hanani, Canad J Math 12 pp 145– (1960) |
| [6] | and Steiner quadruple systems, In: Contemporary Design Theory, and (Editors), Wiley, New York, 1992, 205-240. · Zbl 0765.05017 |
| [7] | Maric, J Lightwave Technol 16 pp 9– (1998) |
| [8] | Maric, J Lightwave Technol 14 pp 2149– (1996) |
| [9] | Mendelsohn, Utilitas Math 1 pp 5– (1972) |
| [10] | Salehi, IEEE Trans. Commun. 37 pp 824– (1989) |
| [11] | Peltesohn, Compositio Math 6 pp 251– (1939) |
| [12] | Phelps, Ars Combin 4 pp 177– (1977) |
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