@article {IOPORT.05903534,
    author       = {Mazumdar, Arya and Roth, Ron M. and Vontobel, Pascal O.},
    title        = {On linear balancing sets.},
    year         = {2010},
    journal      = {Advances in Mathematics of Communications},
    volume       = {4},
    number       = {3},
    issn         = {1930-5346},
    pages        = {345-361},
    publisher    = {Shandong University, Jinan; American Institute of Mathematical Sciences, Springfield, MO},
    doi          = {10.3934/amc.2010.4.345},
    abstract     = {Summary: Let $n$ be an even positive integer and $\Bbb F$ be the field GF(2). A word in $\Bbb F^n$ is called balanced if its Hamming weight is $n/2$. A subset $\cal C\subseteq\Bbb F^n$ is called a balancing set if for every word $\bold y\in\Bbb F^n$ there is a word $\bold x\in \cal C$ such that $\bold y + \bold x$ is balanced. It is shown that most linear subspaces of $\Bbb F^n$ of dimension slightly larger than $\frac{3}{2} \log_2n$ 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 $\Bbb F^n$ 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.},
    identifier   = {05903534},
}