caa a22 4500 445855797 CHVBK 20180317145427.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s00026-011-0092-7 doi (NATIONALLICENCE)springer-10.1007/s00026-011-0092-7 Đoković Dragomir Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut Cyclic ( v [Elektronische Daten] ; r , s ; λ ) Difference Families with Two Base Blocks and v ≤ 50 [Dragomir Đoković] We construct many new cyclic (v; r, s; λ) difference families with v ≥ 2r ≥ 2s ≥ 4 and v ≤ 50. In particular, we construct the difference families with parameters (45; 18, 10; 9), (45; 22, 22; 21), (47; 21, 12; 12), (47; 19, 15; 12), (47; 22, 14; 14), (48; 20, 10; 10), (48; 24, 4; 12), (50; 25, 20; 20), for which the existence question was an open problem. We point out that the (45; 22, 22; 21) difference family gives a balanced incomplete block design (BIBD) with parameters v = 45, b = 90, r = 44, k = 22, and λ = 21, and that the one with parameters (50; 25, 20; 20) gives a pair of binary sequences of length 50 with zero periodic autocorrelation function (the periodic analog of a Golay pair). The new SDSs include nine new D-optimal designs. A normal form for cyclic difference families (with base blocks of arbitrary sizes) is proposed and used effectively in compiling our selective listings in Tables 3-6 of known and new difference families in the above range. Springer Basel AG, 2011 difference family nationallicence supplementary difference sets nationallicence balanced incomplete block designs nationallicence genetic algorithm nationallicence Annals of Combinatorics SP Birkhäuser Verlag Basel 15/2(2011-06-01), 233-254 0218-0006 15:2<233 2011 15 26 https://doi.org/10.1007/s00026-011-0092-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00026-011-0092-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Đoković Dragomir Department of Pure Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada aut NATIONALLICENCE 773 0- Annals of Combinatorics SP Birkhäuser Verlag Basel 15/2(2011-06-01), 233-254 0218-0006 15:2<233 2011 15 26 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer