2002
DOI: 10.1006/jcta.2001.3219
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On a Particular Class of Minihypers and Its Applications

Abstract: A particular class of minihypers was studied previously by the authors (in press, Des. Codes Cryptogr.). For q square, this paper improves the results of that work, under the assumption that no weights occur in the minihyper. Using the link between these minihypers and maximal partial s-spreads of PG(N, q), (s+1) | (N+1), the findings on minihypers translate immediately into results on the extendability of partial s-spreads with small positive deficiency. Other applications of this characterisation of minihype… Show more

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Cited by 28 publications
(55 citation statements)
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“…By a classification result about minihypers of [30], it is possible to describe the set of multiple points:…”
Section: Theorem 34mentioning
confidence: 99%
“…By a classification result about minihypers of [30], it is possible to describe the set of multiple points:…”
Section: Theorem 34mentioning
confidence: 99%
“…We note that variants of the lemmas, either of smaller total weight or non-weighted versions or statements without proofs, can be found in the literature, e.g. in [9], [12], and [13].…”
Section: Technical Lemmasmentioning
confidence: 99%
“…To state the result, we define a concept which generalizes the Belov, Logachev, and Sandimirov construction. Our definition is a generalization of a similar definition from [9]. Let S 1 , .…”
mentioning
confidence: 99%
“…In the remainder of this article, we will only consider minihypers of this form. The next result of [10] is fundamental for the induction arguments used in the lemmas and theorem which follow.…”
mentioning
confidence: 99%
“…Lemma 2.5 (Govaerts and Storme [10]) Let (F, w) be a {δv µ+1 , δv µ ; n, q}-minihyper satisfying 0 δ (q + 1)/2, 0 µ n − 1, and containing a µ-space π µ . Then the minihyper (F , w ) defined by the weight function w , where…”
mentioning
confidence: 99%