### 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 .