## Access

You are not currently logged in.

Access JSTOR through your library or other institution:

Journal Article

# 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
Stable URL: http://www.jstor.org/stable/25049887
Page Count: 16

#### Select the topics that are inaccurate.

Cancel
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.

• 377
• 378
• 379
• 380
• 381
• 382
• 383
• 384
• 385
• 386
• 387
• 388
• 389
• 390
• 391
• 392
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7962742447853088, "perplexity": 1706.7412851350846}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218203536.73/warc/CC-MAIN-20170322213003-00115-ip-10-233-31-227.ec2.internal.warc.gz"}