4,424 research outputs found
Witness sets
Given a set C of binary n-tuples and c in C, how many bits of c suffice to
distinguish it from the other elements in C? We shed new light on this old
combinatorial problem and improve on previously known bounds.Comment: Coding theory and applications, Espagne (2008
Generalized Effective Reducibility
We introduce two notions of effective reducibility for set-theoretical
statements, based on computability with Ordinal Turing Machines (OTMs), one of
which resembles Turing reducibility while the other is modelled after Weihrauch
reducibility. We give sample applications by showing that certain (algebraic)
constructions are not effective in the OTM-sense and considerung the effective
equivalence of various versions of the axiom of choice
A Fourier analytic approach to the problem of mutually unbiased bases
We give an entirely new approach to the problem of mutually unbiased bases
(MUBs), based on a Fourier analytic technique in additive combinatorics. The
method provides a short and elegant generalization of the fact that there are
at most MUBs in \Co^d. It may also yield a proof that no complete
system of MUBs exists in some composite dimensions -- a long standing open
problem.Comment: 11 page
On Burst Error Correction and Storage Security of Noisy Data
Secure storage of noisy data for authentication purposes usually involves the
use of error correcting codes. We propose a new model scenario involving burst
errors and present for that several constructions.Comment: to be presented at MTNS 201
- …