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

Abstract – This paper introduces some foundations of wavelets over Galois fields. Standard orthogonal finite-field wavelets (FFWavelets) including FF-Haar and FFDaubechies are derived. Non-orthogonal FFwavelets such as B-spline over GF(p) are also considered. A few examples of multiresolution analysis over Finite fields are presented showing how to perform Laplacian pyramid filtering of finite ...

As a finite dimensional linear space over the rational number field Q, an algebraic number field is of particular importance and interest in mathematics and engineering. Algorithms using algebraic number fields can be efficiently implemented involving only integer arithmetics. We observe that all known finitely supported orthogonal wavelet low-pass filters in the literature have coefficients co...