The shift bound for abelian codes and generalizations of the Donoho-Stark uncertainty principle
| Autor: | Qing Xiang, Tao Feng, Henk D. L. Hollmann |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Physics
Mathematics::Functional Analysis Uncertainty principle Mathematics::Commutative Algebra Generalization 020206 networking & telecommunications Field (mathematics) 02 engineering and technology Function (mathematics) Library and Information Sciences Computer Science Applications Combinatorics symbols.namesake Fourier transform FOS: Mathematics 0202 electrical engineering electronic engineering information engineering symbols Mathematics - Combinatorics Combinatorics (math.CO) Algebra over a field Abelian group Information Systems |
| Popis: | Let $G$ be a finite abelian group. If $f: G\rightarrow \bC$ is a nonzero function with Fourier transform $\hf$, the Donoho-Stark uncertainty principle states that $|\supp(f)||\supp(\hf)|\geq |G|$. The purpose of this paper is twofold. First, we present the shift bound for abelian codes with a streamlined proof. Second, we use the shifting technique to prove a generalization and a sharpening of the Donoho-Stark uncertainty principle. In particular, the sharpened uncertainty principle states, with notation above, that $|\supp(f)||\supp(\hf)|\geq |G|+|\supp(f)|-|H(\supp(f))|$, where $H(\supp(f))$ is the stabilizer of $\supp(f)$ in $G$. 14 pages, submitted |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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