Cyclic Polygonal Designs with Block Size 3 and λ = 1 for Joint Distance α = 6 to 16

Abstract

Stufken (1993) first introduced cyclic polygonal designs (CPDs) (in terms of cyclic balanced sampling plans excluding adjacent units (CBSAs)) for joint distance α ≥ 2. Wei (2002) first suggested the use of Langford sequence for the existence and construction of CPDs with block size k = 3 and λ = 1 for arbitrary α. Zhang and Chang (2005b) used Langford and extended Langford sequence, and constructed CPDs (in terms of CBSAs) with block size k = 3 and λ = 1 for joint distance α = 2, 3. Zhang and Chang (2006) also constructed CPDs by using Langford sequence with k = 3 and λ = 1 for joint distance α = 4. Mandal, Parsad and Gupta (2008a) used symmetrically repeated differences and linear programming approach and gave a catalog of CPDs with k = 3, and λ = 1 for joint distance α = 2, 3, 4 and for some v. In this paper, we use the method of cyclic shifts and constructed CPDs with k = 3 and λ = 1 for joint distance α = 6 to 16. A catalog of non-fractional and fractional (or smaller ) CPDs for v ≤ 100 treatments is compiled.

New optimal error-correcting codes for crosstalk avoidance in on-chip data buses

“…. , 16, the existence of circular BSAs were completely determined if the BSAs have a full cyclic automorphism group [25,31,33] (the so called Cyclic Polygonal Designs or cyclic BSA). The case when k = 4 was considered in [34].…”

Ratio Type Estimator for Balanced Sampling Plan excluding Adjacent Units

“…Colbourn and Ling (1998, 1999) and Tahir et al (2010Tahir et al ( , 2012 suggested some techniques to obtain BSA plans with the assumption that the population have a circular ordering. They constructed all the polygonal designs for 𝜈 ≤ 100, 𝑘 = 3 for all permissible 𝑚 using the approach.…”