On linear balancing sets

Authors:
Arya Mazumdar;Ron M. Roth;Pascal O. Vontobel
Affiliations:
Department of ECE, University of Maryland, College Park, MD;Computer Science Department, Technion, Haifa, Israel;Information Theory Research Group, Hewlett-Packard Laboratories, Palo Alto, CA
Venue:
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Year:
2009

Citing 4
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Abstract

Let n be an even positive integer and F be the field GF(2). A word in Fn is called balanced if its Hamming weight is n/2. A subset C ⊆ Fn is called a balancing set if for every word y ∈ Fn there is a word x ∈ C such that y + x is balanced. It is shown that most linear subspaces of Fn of dimension slightly larger than 3/2 log2 n are balancing sets. An application of linear balancing sets is presented for designing efficient error-correcting coding schemes in which the codewords are balanced.