18 research outputs found

    Author index to volume 185 (1998)

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    The order of the automorphism group of a binary qq-analog of the Fano plane is at most two

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    It is shown that the automorphism group of a binary qq-analog of the Fano plane is either trivial or of order 22.Comment: 10 page

    Matroids with nine elements

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    We describe the computation of a catalogue containing all matroids with up to nine elements, and present some fundamental data arising from this cataogue. Our computation confirms and extends the results obtained in the 1960s by Blackburn, Crapo and Higgs. The matroids and associated data are stored in an online database, and we give three short examples of the use of this database.Comment: 22 page

    Nonexistence Certificates for Ovals in a Projective Plane of Order Ten

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    In 1983, a computer search was performed for ovals in a projective plane of order ten. The search was exhaustive and negative, implying that such ovals do not exist. However, no nonexistence certificates were produced by this search, and to the best of our knowledge the search has never been independently verified. In this paper, we rerun the search for ovals in a projective plane of order ten and produce a collection of nonexistence certificates that, when taken together, imply that such ovals do not exist. Our search program uses the cube-and-conquer paradigm from the field of satisfiability (SAT) checking, coupled with a programmatic SAT solver and the nauty symbolic computation library for removing symmetries from the search.Comment: Appears in the Proceedings of the 31st International Workshop on Combinatorial Algorithms (IWOCA 2020

    LinCode - computer classification of linear codes

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    We present an algorithm for the classification of linear codes over finite fields, based on lattice point enumeration. We validate a correct implementation of our algorithm with known classification results from the literature, which we partially extend to larger ranges of parameters.Comment: 12 pages, 5 table

    Maximal integral point sets in affine planes over finite fields

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    Motivated by integral point sets in the Euclidean plane, we consider integral point sets in affine planes over finite fields. An integral point set is a set of points in the affine plane Fq2\mathbb{F}_q^2 over a finite field Fq\mathbb{F}_q, where the formally defined squared Euclidean distance of every pair of points is a square in Fq\mathbb{F}_q. It turns out that integral point sets over Fq\mathbb{F}_q can also be characterized as affine point sets determining certain prescribed directions, which gives a relation to the work of Blokhuis. Furthermore, in one important sub-case integral point sets can be restated as cliques in Paley graphs of square order. In this article we give new results on the automorphisms of integral point sets and classify maximal integral point sets over Fq\mathbb{F}_q for q≤47q\le 47. Furthermore, we give two series of maximal integral point sets and prove their maximality.Comment: 18 pages, 3 figures, 2 table

    Computer classification of linear codes

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    We present algorithms for classification of linear codes over finite fields, based on canonical augmentation and on lattice point enumeration. We apply these algorithms to obtain classification results over fields with 2, 3 and 4 elements. We validate a correct implementation of the algorithms with known classification results from the literature, which we partially extend to larger ranges of parameters.Comment: 18 pages, 9 tables; this paper is a merge and extension of arXiv:1907.10363 and arXiv:1912.0935
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