A subspace code of size 333 in the setting of a binary q-analog of the Fano plane

Daniel Heinlein*, Michael Kiermaier, Sascha Kurz, Alfred Wassermann

*Corresponding author for this work

    Research output: Contribution to journalArticleScientificpeer-review

    4 Citations (Scopus)

    Abstract

    We show that there is a binary subspace code of constant dimension 3 in ambient dimension 7, having minimum subspace distance 4 and cardinality 333, i.e., 333≤A2(7,4;3), which improves the previous best known lower bound of 329. Moreover, if a code with these parameters has at least 333 elements, its automorphism group is in one of 31 conjugacy classes. This is achieved by a more general technique for an exhaustive search in a finite group that does not depend on the enumeration of all subgroups.

    Original languageEnglish
    Pages (from-to)457-475
    Number of pages19
    JournalAdvances in Mathematics of Communications
    Volume13
    Issue number3
    DOIs
    Publication statusPublished - Aug 2019
    MoE publication typeA1 Journal article-refereed

    Keywords

    • Finite groups
    • finite projective spaces
    • constant dimension codes
    • subspace codes
    • subspace distance
    • combinatorics
    • computer search
    • AUTOMORPHISM GROUP
    • PROJECTIVE SPACES
    • CONSTRUCTION
    • GEOMETRIES
    • DESIGNS

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