In all of the following definitions, the term "distance" refers to "relative Hamming distance".
Given a matrix , let denote the distance from to the nearest codeword of . Let denote the average distance of a row of to , and let denote the average distance of a column of to . Finally, let denote the average of and .
The tensor product is said to be -robust iff for every matrix we have that .
The question is, under what conditions the tensor product is -robust for some constant .
The formal definition of robustness, and of the problem
In all of the following definitions, the term "distance" refers to "relative Hamming distance".
Given a matrix
, let
denote the distance from
to the nearest codeword of
. Let
denote the average distance of a row of
to
, and let
denote the average distance of a column of
to
. Finally, let
denote the average of
and
.
The tensor product
is said to be
-robust iff for every matrix
we have that
.
The question is, under what conditions the tensor product
is
-robust for some constant
.