Primitive Ovoids in O+8(q)

Gunawardena, Athula

doi:10.1006/jcta.1999.3004

Cited by 6 publications

(5 citation statements)

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“…Gunawardena [17] has extended the Kleidman's results by determining the ovoids in O + 8 (q) which admits a primitive group. Bamberg and Pentilla [3] recently classified the ovoids and spreads in finite polar spaces which are stabilized by an insoluble transitive group of collineations, as a more general classification of m-systems admitting such groups.…”

Section: Q(λx) = λ 2 Q(x)mentioning

confidence: 98%

“…According to [8], the only O + 8 (5) ovoids are the Kantor ovoid (2-transitive) [19], the Cooperstein ovoid [10] which is the only primitive ovoid that is not 2-transitive [17,3], and the binary ovoid constructed from the E8 root lattice [9,23]. In Table 5, we show the invariants for the O We have also found examples of orthogonal spaces in which our invariant is not complete.…”

Section: Ovoidal Graph Invariantsmentioning

confidence: 99%

“…Consider the two equations (16) and (17) from above. Add equation (16) multiplied by v to equation (17) multiplied by u to eliminate w and obtain…”

Section: Thas-kantor Ovoid In O 7 (Q) Q =mentioning

confidence: 99%

“…Note that the isomorphism invariant |P| is sufficient to identify the ovoids in O 5 (q) where q = 9, 25 or 27. (2,27), (3, 60), (7, 3)} {(1, 395), (2,27), (3, 60), (7, 3)} O 13 928 464 464 {(1, 348), (2, 84), (3,12), (4,11), (6, 9)} {(1, 358), (2,66), (3,9), (4,24), (5,6) (2,104), (3,13), (4,8), (5, 1), (6, 2)} {(1, 354), (2,104), (3,13), (4,8), (5, 1), (6, 2)} O 17 796 398 398 {(1, 265), (2,54), (3,48), (4,24), (5,6), (7, 1)} {(1, 265), (2,54), (3,48), (4,24), (5,6), (7, 1)} O 18 688 344 344 {(1, 144), (2,144), (3,…”

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On incidence structures of nonsingular points and hyperbolic lines of ovoids in finite orthogonal spaces

Fuelberth

Gunawardena

Shaffer

2009

Des. Codes Cryptogr.

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The revisions were made according to the referees' suggestions as mentioned in the bold and italic statements below.Reviewer #1: You may have missed the recent paper A classification of transitive ovoids, spreads and m-systems of polar spaces, Forum Mathematicum 21(2009), 181-216 which classifies primitive ovoids in all classical polar spaces provided they do not have cardinality a prime number. I recommend that you add it to your list of references, and refer to it in Section 1 (after discussing Kleidman's result) and/or in Section 5, when referring to your own result about primitive ovoids from [15].Added to the list of references. Refered to it in Section 1 and Section 5.Typos : voids for ovoids (page 13, line 9), bipartitie for bipartite (page 6, line 21); there is no Tits ovoid over the field of order 27 (page 13, line 28), but they should have occurred two sentences earlier in the list of known ovoids. Page 13, line 27, you need two definite articles added : For q=25 the only... For q=27 the only... Typos were corrected. Reviewer 2The authors introduce new invariants of ovoids in finite orthogonal spaces. This paper is suitable for publication in DCC provided the following changes are made: p3 l 49 reference to [19] should be replaced by: Charnes and Dempwolff [CD7], and this reference should be included in the bibliography. It should also be mentioned that fingerprints give an effective method of calculating the automorphism groups of ovoids. The following typos were corrected. Abstract. We study the point-line incidence structures of nonsingular points and hyperbolic secant lines associated with ovoids in finite orthogonal spaces. We show that these incidence structures frequently produce partial linear spaces and the parameters of the bipartite graphs (called ovoidal graphs) associated with these structures produce simple and effective isomorphism invariants to distinguish non-isomorphic ovoids. We prove explicit formulas for these isomorphism invariants for a number of infinite families of 2-transitive ovoids. Abstract. We study the point-line incidence structures of nonsingular points and hyperbolic secant lines associated with ovoids in finite orthogonal spaces. We show that these incidence structures frequently produce partial linear spaces and the parameters of the bipartite graphs (called ovoidal graphs) associated with these structures produce simple and effective isomorphism invariants to distinguish non-isomorphic ovoids. We prove explicit formulas for these isomorphism invariants for a number of infinite families of 2-transitive ovoids.

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Section: Q(λx) = λ 2 Q(x)mentioning

confidence: 98%

Section: Ovoidal Graph Invariantsmentioning

confidence: 99%

“…Consider the two equations (16) and (17) from above. Add equation (16) multiplied by v to equation (17) multiplied by u to eliminate w and obtain…”

Section: Thas-kantor Ovoid In O 7 (Q) Q =mentioning

confidence: 99%

mentioning

confidence: 99%

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On incidence structures of nonsingular points and hyperbolic lines of ovoids in finite orthogonal spaces

Fuelberth

Gunawardena

Shaffer

2009

Des. Codes Cryptogr.

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“…By a beautiful result of A. Ovoids of finite classical polar spaces have been intensively investigated, especially in the last two decades, see [1], [3], [4], [5], [9], [12], [13], [14] and the recent survey paper [15]. This is a generalisation of Segre's famous theorem [11] stating that every oval in PG (2, q), with q odd, is a conic.…”

Section: Introductionmentioning

confidence: 99%