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# On Three Level Symmetrical Factorial Designs and Ternary Group Codes

B. R. Gulati and E. G. Kounias
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 35, No. 3, Dedicated to the Memory of P. C. Mahalanobis (Sep., 1973), pp. 377-392
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25049887
Page Count: 16
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## Abstract

Consider a finite (t+r-1)-dimensional projective space PG(t+r-1, s) based on the Galois field GF(s) of order $s=p^{h}$ (where p and h are positive integers and p is the prime characteristic of the field). A set of k distinct points in PG(t+r-1, s), no t linearly dependent, is called a (k, t)-set and such a set is said to be maximal if there exists no other $(k_{1},t)\text{-}{\rm set}$ with $k_{1}>k$. The number of points in a maximal set is denoted by $m_{t}(t+r,s)$. It is the purpose of this paper to investigate $m_{t}(t+r,3)$ in certain relationships of t and r and establish conditions under which the set of $E_{i}$, i = 1, 2,..., t+r, where $E_{i}$ is a point with a one in i-th position and zeros elsewhere can be augmented. The problem has several applications in the theory of fractionally replicated designs and construction of ternary group codes in information theory.

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