On linear balancing sets
Arya Mazumdar, Ron M. Roth, Pascal O. Vontobel · 2009
Let n be an even positive integer and F be the field GF(2). A word in Fnis called balanced if its Hamming weight is n/2. A subset C ¿ Fnis called a balancing set if for every word y ¿ Fnthere is a word x ¿ C such that y + x is balanced. It is shown that most linear subspaces of Fnof dimension slightly larger than 3/2 log2n are balancing sets. An application of linear balancing sets is presented for designing efficient error-correcting coding schemes in which the codewords are balanced.