Geometry for Teachers - Nowlan, Robert A.; Washburn, Robert M. (1973)
Keywords: Geometry; dept.mat; faculty_collection

On maximal t-linearly independent sets - Gulati, Bodh Raj; Johnson, Bruce McK.; Koehn, Uwe (Journal of Combinatorial Theory, Series A, 1973)
Consider a finite t + r − 1 dimensional projective space PG(t + r − 1, s) over a Galois field GF(s) of order s = ϱh, where ϱ and h are positive integers and ϱ is the prime characteristic of the field. A collection of k points in PG (t + r − 1, s) constitutes an L(t, k)-set if no t of them are linearly dependent. An L(t, k)-set is maximal if there exists no other L(t, k′)-set with k′ > k. The largest k for which an L(t, k)-set exists is denoted by Mt(t + r, s). K. A. Bush [3] established that Mt(t, s) = t + 1 for t ⩾ s. The purpose of this paper is to generalize this result and study Mt(t + r, s) for t, r, and s in certain relationships.
Keywords: dept.mat; information; theoretical study

An apparently algebraic property of the integers - Berlinghoff, W P (Mathematics Magazine, 1973)
Keywords: dept.mat

Maximal sets of points in finite projective space, no t-linearly dependent - Gulati, Bodh Raj; Kounias, E G (Journal of Combinatorial Theory, Series A, 1973)
Consider a finite (t + r - 1)-dimensional projective space PG(t + r - 1, s) based on the Galois field GF(s), where s is prime or power of a prime. 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 it is not contained in any other (k*, t)-set with k* > k. The number of points in a maximal (k, t)-set with the largest k is denoted by mt(t + r, s). Our purpose in the paper is to investigate the conditions under which two or more points can be adjoined to the basic set of Ei, i = 1, 2, ..., t + r, where Ei is a point with one in i-th position and zeros elsewhere. The problem has several applications in the theory of fractionally replicated designs and information theory. © 1973.
Keywords: dept.mat; melampolide

3 Level Symmetrical Factorial Designs and Ternary Group Codes - Gulati, BR; Kounias, EG (Sankhya-the Indian Journal of Statistics Series A, 1973)
Keywords: dept.mat; ⛔ No DOI found