Nonfactorizable nonsingular hypercubes

David Glynn

    Research output: Contribution to journalArticle

    Abstract

    We investigate nonsingular hypercubes, and prove several results, stating a condition for a hypercube to be the product of hypercubes of smaller dimensions. There is a shortage of higher dimensional nonsingular hypercubes in the literature. However, we show that the product of two nonsingular hypercubes is always nonsingular. Then we show how to construct four-dimensional nonsingular hypercubes that are not the products of two three-dimensional hypercubes. It is noted that higher dimensional nonsingular hypercubes, that are not products of smaller ones, correspond to many semifields.

    Original languageEnglish
    Pages (from-to)195-203
    Number of pages9
    JournalDesigns Codes and Cryptography
    Volume68
    Issue number1-3
    DOIs
    Publication statusPublished - Jul 2013

    Keywords

    • Associative law
    • Cube
    • Hypercube
    • Inner product
    • Multilinear
    • Nonsingular
    • Quadric
    • Semifield

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