Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Corrections and additions to `` Pieces of $2^d$: existence and
  uniqueness for Barnes-Wall and Ypsilanti lattices. ''   Mainly, we correct the uniqueness result by adding a projection requirement
to condition X and give a better proof for the equivalence of commutator
density, 2/4-generation and 3/4-generation.

36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th