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September, 1973 On a New Type of $m$-Class Cyclic Association Scheme and Designs Based on the Scheme
G. M. Saha, A. C. Kulshreshtha, A. Dey
Ann. Statist. 1(5): 985-990 (September, 1973). DOI: 10.1214/aos/1176342521


A new type of $m$-class cyclic association scheme is defined for $v$ objects, where $v$ is either a prime or power of a prime. The two cases, when $v$ is even and when $v$ is odd are dealt with separately. A simple method of construction of PBIB designs based on this scheme is proposed. The PBIB designs presented in this paper have cyclic solutions and are obtainable through more than one initial block. The proposed scheme has been called an $NC_m$ association scheme and the number of independent $p_{jk}$'s for this scheme is obtained.


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G. M. Saha. A. C. Kulshreshtha. A. Dey. "On a New Type of $m$-Class Cyclic Association Scheme and Designs Based on the Scheme." Ann. Statist. 1 (5) 985 - 990, September, 1973.


Published: September, 1973
First available in Project Euclid: 12 April 2007

zbMATH: 0274.62055
MathSciNet: MR433755
Digital Object Identifier: 10.1214/aos/1176342521

Keywords: cosets , Cyclic association scheme , initial block , PBIB designs

Rights: Copyright © 1973 Institute of Mathematical Statistics


Vol.1 • No. 5 • September, 1973
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