Designs from matroids

T. Britz, Gordon Royle, K. Shiromoto

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)


    This paper presents new connections between designs and matroids. We generalize the Assmus–Mattson theorem and another coding-theoretical theorem with respect to matroids, and thereby present new sufficient conditions for obtaining $t$-designs from matroids. These conditions may be relaxed for some self-dual matroids. We use our results to prove new constructions of $t$-designs from linear codes, including several new extensions and variants of the Assmus–Mattson theorem. We also present weighted $t$-designs which generalize $t$-designs. New $t$-designs are obtained from our results.
    Original languageEnglish
    Pages (from-to)1082-1099
    JournalSIAM Journal on Discrete Mathematics
    Issue number2
    Publication statusPublished - 2009


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