Lower Bounds for Constant Query Affine-Invariant LCCs and LTCs

Lower Bounds for 2-Query LCCs over Large Alphabet

A locally correctable code (LCC) is an error correcting code that allows correction of any arbitrary coordinate of a corrupted codeword by querying only a few coordinates. We show that any 2query locally correctable code C : {0, 1} → Σ that can correct a constant fraction of corrupted symbols must have n > exp(k/ log |Σ|) under the assumption that the LCC is zero-error. We say that an LCC is ze...

Lower bounds for multivariate approximation by affine-invariant dictionaries

The problem of approximating locally smooth multivariate functions by linear combinations of elements from an affine-invariant redundant dictionary is considered. Augmenting recent upper bound results for approximation, we establish lower bounds on the performance of such schemes. The lower bounds are tight to within a logarithmic factor in the number of elements used in the approximation. Usin...

Lower Bounds for the Disk Packing Constant

An osculatory packing of a disk, U, is an infinite sequence of disjoint disks, ¡ U„ \, contained in U, chosen so that, for n S 2, (/» has the largest possible radius, r„, of all disks fitting in U\(Ui \J ••• KJ i/„_i). The exponent of the packing, S, is the least upper bound of numbers, t, such that 2Z r\, = <*>. Here, we present a number of methods for obtaining lower bounds for S, based on ob...

New lower bounds for constant weight codes

with M (which is expected). However, as M increases beyond Ahstrart -Some new lower bounds are given for A(n,4, IV), the maximum number of codewords in a binary code of length n, min imum distance 4, and constant weight IV. In a number of cases the results significantly 1.0 improve on the best bounds previously known. h=O 1 .

Lower Bounds for Constant Depth Circuits