Almost orthogonal subsets of vector spaces over finite fields

Almost orthogonal subsets of vector spaces over finite fields

We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of Rosenfeld and an almost version of a theorem of Berlekamp.

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Veröffentlicht in:European journal of combinatorics 2022-06, Vol.103, p.103515, Article 103515
Hauptverfasser: Mohammadi, Ali, Petridis, Giorgis
Format: Artikel
Sprache:eng
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Zusammenfassung:We prove various results on the size and structure of subsets of vector spaces over finite fields which, in some sense, have too many mutually orthogonal pairs of vectors. In particular, we obtain sharp finite field variants of a theorem of Rosenfeld and an almost version of a theorem of Berlekamp.
ISSN:0195-6698
1095-9971
DOI:10.1016/j.ejc.2022.103515