On a geometrical method of construction of maximal t-linearly independent sets |
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Authors: | Noboru Hamada Fumikazu Tamari |
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Affiliation: | Department of Mathematics, Faculty of Science, Hiroshima University, Hiroshima, Japan;Department of Mathematics, Fukuoka University of Education, Munakata, Fukuoka, Japan |
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Abstract: | The problem of constructing a maximal t-linearly independent set in V(r; s) (called a maximal Lt(r, s)-set in this paper) is a very important one (called a packing problem) concerning a fractional factorial design and an error correcting code where V(r; s) is an r-dimensional vector space over a Galois field GF(s) and s is a prime or a prime power. But it is very difficult to solve it and attempts made by several research workers have been successful only in special cases.In this paper, we introduce the concept of a {Σα=1kwα, m; t, s}-min · hyper with weight (w1, w2,…, wk) and using this concept and the structure of a finite projective geometry PG(n ? 1, s), we shall give a geometrical method of constructing a maximal Lt(t + r, s)-set with length t + r + n for any integers r, n, and s such that n ? 3, n ? 1 ? r0 ? n + s ? 2 and r1 ? 1, where r = (r1 + 1)vn?1 ? r0 and . |
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