Periodic Golay pairs and pairwise balanced designs

2022 ◽  
Author(s):  
Dean Crnković ◽  
Doris Dumičić Danilović ◽  
Ronan Egan ◽  
Andrea Švob
Keyword(s):  
Pairwise Balanced Designs ◽  
Balanced Designs

scholarly journals Pairwise balanced designs and sigma clique partitions

2016 ◽  
Vol 339 (5) ◽  
pp. 1450-1458 ◽  
Author(s):  
Akbar Davoodi ◽  
Ramin Javadi ◽  
Behnaz Omoomi
Keyword(s):  
Pairwise Balanced Designs ◽  
Balanced Designs

scholarly journals Pairwise balanced designs from finite fields

1999 ◽  
Vol 208-209 ◽  
pp. 103-117 ◽  
Author(s):  
Marco Buratti
Keyword(s):  
Finite Fields ◽  
Pairwise Balanced Designs ◽  
Balanced Designs

scholarly journals Some Pairwise Balanced Designs

10.37236/1491 ◽  
1999 ◽  
Vol 7 (1) ◽  
Author(s):  
Malcolm Greig
Keyword(s):  
Block Design ◽  
Basis Sets ◽  
Combinatorial Designs ◽  
Pairwise Balanced Design ◽  
Balanced Design ◽  
Pairwise Balanced Designs ◽  
Balanced Designs ◽  
Block Sizes

A pairwise balanced design, $B(K;v)$, is a block design on $v$ points, with block sizes taken from $K$, and with every pair of points occurring in a unique block; for a fixed $K$, $B(K)$ is the set of all $v$ for which a $B(K;v)$ exists. A set, $S$, is a PBD-basis for the set, $T$, if $T=B(S)$. Let $N_{a(m)}=\{n:n\equiv a\bmod m\}$, and $N_{\geq m}=\{n:n\geq m\}$; with $Q$ the corresponding restriction of $N$ to prime powers. This paper addresses the existence of three PBD-basis sets. 1. It is shown that $Q_{1(8)}$ is a basis for $N_{1(8)}\setminus E$, where $E$ is a set of 5 definite and 117 possible exceptions. 2. We construct a 78 element basis for $N_{1(8)}$ with, at most, 64 inessential elements. 3. Bennett and Zhu have shown that $Q_{\geq8}$ is a basis for $N_{\geq8}\setminus E'$, where $E'$ is a set of 43 definite and 606 possible exceptions. Their result is improved to 48 definite and 470 possible exceptions. (Constructions for 35 of these possible exceptions are known.) Finally, we provide brief details of some improvements and corrections to the generating/exception sets published in The CRC Handbook of Combinatorial Designs.

scholarly journals Resolvable (r, λ)-designs and the Fisher inequality

1979 ◽  
Vol 28 (4) ◽  
pp. 471-478 ◽  
Author(s):  
S. A. Vanstone
Keyword(s):  
Block Design ◽  
Incomplete Block ◽  
Balanced Incomplete Block Design ◽  
Incomplete Block Design ◽  
Pairwise Balanced Designs ◽  
Balanced Designs ◽  
Similar Inequality ◽  
Balanced Incomplete Block

AbstractIt is well known that in any (v, b, r, k, λ) resolvable balanced incomplete block design that b≧ ν + r − l with equality if and only if the design is affine resolvable. In this paper, we show that a similar inequality holds for resolvable regular pairwise balanced designs ((ρ, λ)-designs) and we characterize those designs for which equality holds. From this characterization, we deduce certain results about block intersections in (ρ, λ)-designs.

scholarly journals Pairwise balanced designs with odd block sizes exceeding five

1990 ◽  
Vol 84 (1) ◽  
pp. 47-62 ◽  
Author(s):  
R.C. Mullin ◽  
D.R. Stinson
Keyword(s):  
Pairwise Balanced Designs ◽  
Balanced Designs ◽  
Block Sizes

DIRECTED PAIRWISE BALANCED DESIGNS WITH BLOCK SIZES FROM SUBSETS OF {3, 4, …, 10} WHICH CONTAIN 3

2009 ◽  
Vol 01 (04) ◽  
pp. 519-529
Author(s):  
WEIWEI DING ◽  
JIANMIN WANG
Keyword(s):  
Pairwise Balanced Designs ◽  
Single Deletion ◽  
Balanced Designs ◽  
Block Sizes

In this paper we determine completely the spectra of directed pairwise balanced designs with block sizes from any subset of {3, 4, …, 10} which contains 3. Such designs can be used to construct single-deletion/insertion-correcting codes in which the lengths of the codewords may be different.

Four pairwise balanced designs

1991 ◽  
Vol 1 (1) ◽  
pp. 63-68 ◽  
Author(s):  
E. R. Lamken ◽  
W. H. Mills ◽  
R. M. Wilson
Keyword(s):  
Pairwise Balanced Designs ◽  
Balanced Designs
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