Title :
On linear balancing sets
Author :
Mazumdar, Arya ; Roth, Ron M. ; Vontobel, Pascal O.
Author_Institution :
Dept. of ECE, Univ. of Maryland, College Park, MD, USA
fDate :
June 28 2009-July 3 2009
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.
Keywords :
Hamming codes; error correction codes; linear codes; Hamming weight; error-correcting coding schemes; even positive integer; linear balancing set; linear subspaces; Computer science; Educational institutions; Encoding; Error correction codes; Galois fields; Hamming distance; Hamming weight; Information theory; Laboratories; Redundancy;
Conference_Titel :
Information Theory, 2009. ISIT 2009. IEEE International Symposium on
Conference_Location :
Seoul
Print_ISBN :
978-1-4244-4312-3
Electronic_ISBN :
978-1-4244-4313-0
DOI :
10.1109/ISIT.2009.5205879
