Fuglede’s conjecture fails in 4 dimensions over odd prime fields
نویسندگان
چکیده
منابع مشابه
Geometric Codes over Fields of Odd Prime Power Order
We obtain improved bounds for the minimum weight of the dual codes associated with the codes from finite geometries in the case of odd order, and some results that apply also to the dual codes of non-desarguesian planes of odd order.
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n0 = min{n ∈ N | f(n) > n + 1}, then the proof of Kahn and Kalai gives n0 ≤ 1325. On the other hand we know only that n0 ≥ 4 (Perkal [7]; Eggleston [3]). It is of interest where n0 lies. The upper bound on n0 was improved to n0 ≤ 946 (Nilli [6]), n0 ≤ 561 (Raigorodski [8]), n0 ≤ 560 (Weißbach [9]), and n0 ≤ 323 (Hinrichs [4]). In fact, we know that f(n) > n + 1 for all n ≥ 323. Here we show tha...
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In a complex vector space of dimension N , by a full set of mutually unbiased bases (MUB’s) we mean a set of N+1 orthonormal bases such that the modulus square of the scalar product of any member of one basis with any member of any other basis is equal to 1/N . If we take e to denote the k vector in the α orthonormal basis, then having a full set of MUB’s amounts to having a collection e ; α = ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2020
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.04.026