Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On linear balancing sets   Let n be an even positive integer and F be the field \GF(2). A word in F^n is
called balanced if its Hamming weight is n/2. A subset C \subseteq F^n$ is
called a balancing set if for every word y \in F^n there is a word x \in C such
that y + x is balanced. It is shown that most linear subspaces of F^n of
dimension slightly larger than 3/2\log_2(n) are balancing sets. A
generalization of this result to linear subspaces that are "almost balancing"
is also presented. On the other hand, it is shown that the problem of deciding
whether a given set of vectors in F^n spans a balancing set, is NP-hard. An
application of linear balancing sets is presented for designing efficient
error-correcting coding schemes in which the codewords are balanced.

24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys