Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

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
  • Download ($43.95)
  • Cite this Item
On Three Level Symmetrical Factorial Designs and Ternary Group Codes
Preview not available

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.

Page Thumbnails

  • Thumbnail: Page 
377
    377
  • Thumbnail: Page 
378
    378
  • Thumbnail: Page 
379
    379
  • Thumbnail: Page 
380
    380
  • Thumbnail: Page 
381
    381
  • Thumbnail: Page 
382
    382
  • Thumbnail: Page 
383
    383
  • Thumbnail: Page 
384
    384
  • Thumbnail: Page 
385
    385
  • Thumbnail: Page 
386
    386
  • Thumbnail: Page 
387
    387
  • Thumbnail: Page 
388
    388
  • Thumbnail: Page 
389
    389
  • Thumbnail: Page 
390
    390
  • Thumbnail: Page 
391
    391
  • Thumbnail: Page 
392
    392