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Several new families of c‐Bhaskar Rao designs with block size 4 are constructed. The necessary conditions for the existence of a c‐BRD (υ,4,λ) are that: (1)λmin=?λ/3 ≤ c ≤ λ and (2a) c≡λ (mod 2), if υ > 4 or (2b) c≡ λ (mod 4), if υ = 4 or (2c) c≠ λ ? 2, if υ = 5. It is proved that these conditions are necessary, and are sufficient for most pairs of c and λ; in particular, they are sufficient whenever λ?c ≠ 2 for c > 0 and whenever c ? λmin≠ 2 for c < 0. For c < 0, the necessary conditions are sufficient for υ> 101; for the classic Bhaskar Rao designs, i.e., c = 0, we show the necessary conditions are sufficient with the possible exception of 0‐BRD (υ,4,2)'s for υ≡ 4 (mod 6). © 2002 Wiley Periodicals, Inc. J Combin Designs 10: 361–386, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10009 相似文献
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Necessary conditions for the existence of a super‐simple, decomposable, near‐resolvable ‐balanced incomplete block design (BIBD) whose 2‐component subdesigns are both near‐resolvable ‐BIBDs are (mod ) and . In this paper, we show that these necessary conditions are sufficient. Using these designs, we also establish that the necessary conditions for the existence of a super‐simple near‐resolvable ‐RBIBD, namely (mod ) and , are sufficient. A few new pairwise balanced designs are also given. 相似文献
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We show the necessary conditions are sufficient for the existence of group divisible designs (or PBIBDs) with block size k=3 with three groups of size (n,2,1) for any n≥2 and any two indices with λ1>λ2. 相似文献
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This paper presents a newly constructed zero cross correlation code (ZCC) which is based on BIBD (balanced incomplete block design) code. The ZCC (C, w) code is a family of binary sequences of length C and constant Hamming-weight w. Such codes find applications in spectral amplitude-coding optical code division multiple access (SAC-OCDMA). The constructing ZCC codes have a size of C ? N ÿ w + 1, where N is the number of users and C is any prime number. The proposed construction method is not complicated compared to the existing ones. 相似文献
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E. R. Lamken 《Designs, Codes and Cryptography》1997,11(1):37-71
A generalized balanced tournament design, GBTD(n, k), defined on a kn-set V, is an arrangement of the blocks of a (kn, k, k – 1)-BIBD defined on V into an n × (kn – 1) array such that (1) every element of V is contained in precisely one cell of each column, and (2) every element of V is contained in at most k cells of each row. Suppose we can partition the columns of a GBTD(n, k) into k + 1 sets B1, B2,..., Bk + 1 where |Bi| = n for i = 1, 2,..., k – 2, |Bi| = n–1 for i = k – 1, k and |Bk+1| = 1 such that (1) every element of V occurs precisely once in each row and column of Bi for i = 1, 2,..., k – 2, and (2) every element of V occurs precisely once in each row and column of Bi Bk+1 for i = k – 1 and i = k. Then the GBTD(n, k) is called partitioned and we denote the design by PGBTD(n, k). The spectrum of GBTD(n, 3) has been completely determined. In this paper, we determine the spectrum of PGBTD(n,3) with, at present, a fairly small number of exceptions for n. This result is then used to establish the existence of a class of Kirkman squares in diagonal form. 相似文献
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Spencer P. Hurd 《Discrete Mathematics》2008,308(13):2663-2673
We give some constructions of new infinite families of group divisible designs, GDD(n,2,4;λ1,λ2), including one which uses the existence of Bhaskar Rao designs. We show the necessary conditions are sufficient for 3?n?8. For n=10 there is one missing critical design. If λ1>λ2, then the necessary conditions are sufficient for . For each of n=10,15,16,17,18,19, and 20 we indicate a small minimal set of critical designs which, if they exist, would allow construction of all possible designs for that n. The indices of each of these designs are also among those critical indices for every n in the same congruence class mod 12. 相似文献
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R. Julian R. Abel Norman J. Finizio Malcolm Greig Luis B. Morales 《Designs, Codes and Cryptography》2009,51(1):79-97
(2, 8) Generalized Whist tournament Designs (GWhD) on v players exist only if . We establish that these necessary conditions are sufficient for all but a relatively small number of (possibly) exceptional
cases. For there are at most 12 possible exceptions: {177, 249, 305, 377, 385, 465, 473, 489, 497, 537, 553, 897}. For there are at most 98 possible exceptions the largest of which is v = 3696. The materials in this paper also enable us to obtain four previously unknown (4, 8)GWhD(8n+1), namely for n = 16,60,191,192 and to reduce the list of unknown (4, 8) GWhD(8n) to 124 values of v the largest of which is v = 3696.
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朱烈 《高校应用数学学报(A辑)》1992,(3)
Hanani discussed the existence of balanced incomplete block designs B[7,3;ν] leaving seven open cases of v , five of which were solved by Greig and Yin and Wu. In this paper we shall deal with the last two cases and then complete the existence question. 相似文献
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Eric Merchant 《Designs, Codes and Cryptography》2006,38(2):297-308
If there is a Hadamard design of order n, then there are at least 28n−16−9log n non-isomorphic Hadamard designs of order 2n.
Mathematics Subject Classificaion 2000: 05B05 相似文献