Structural theorems on the distance sets over finite fields
نویسندگان
چکیده
Abstract Let F q \mathbb{F}_{q} be a finite field of order
منابع مشابه
Bertini Theorems over Finite Fields
Let X be a smooth quasiprojective subscheme of P of dimension m ≥ 0 over Fq. Then there exist homogeneous polynomials f over Fq for which the intersection of X and the hypersurface f = 0 is smooth. In fact, the set of such f has a positive density, equal to ζX(m + 1) −1, where ζX(s) = ZX(q −s) is the zeta function of X. An analogue for regular quasiprojective schemes over Z is proved, assuming ...
متن کاملBertini Irreducibility Theorems over Finite Fields
Given a geometrically irreducible subscheme X ⊆ PnFq of dimension at least 2, we prove that the fraction of degree d hypersurfaces H such that H ∩X is geometrically irreducible tends to 1 as d→∞. We also prove variants in which X is over an extension of Fq, and in which the immersion X → PnFq is replaced by a more general morphism.
متن کاملIntegral point sets over finite fields
We consider point sets in the affine plane Fq where each Euclidean distance of two points is an element of Fq . These sets are called integral point sets and were originally defined in m-dimensional Euclidean spaces Em. We determine their maximal cardinality I(Fq , 2). For arbitrary commutative rings R instead of Fq or for further restrictions as no three points on a line or no four points on a...
متن کاملClassical Wavelet Transforms over Finite Fields
This article introduces a systematic study for computational aspects of classical wavelet transforms over finite fields using tools from computational harmonic analysis and also theoretical linear algebra. We present a concrete formulation for the Frobenius norm of the classical wavelet transforms over finite fields. It is shown that each vector defined over a finite field can be represented as...
متن کاملClassical wavelet systems over finite fields
This article presents an analytic approach to study admissibility conditions related to classical full wavelet systems over finite fields using tools from computational harmonic analysis and theoretical linear algebra. It is shown that for a large class of non-zero window signals (wavelets), the generated classical full wavelet systems constitute a frame whose canonical dual are classical full ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2023
ISSN: ['1435-5337', '0933-7741']
DOI: https://doi.org/10.1515/forum-2022-0140