On linear balancing sets

Arya Mazumdar; Ron M. Roth; Pascal O. Vontobel

doi:10.1109/ISIT.2009.5205879

On linear balancing sets

Arya Mazumdar, Ron M. Roth, Pascal O. Vontobel

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Scopus citations

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 F ⁿ is called a balancing set if for every word y ε 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.

Original language	English (US)
Title of host publication	2009 IEEE International Symposium on Information Theory, ISIT 2009
Pages	2699-2703
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2009.5205879
State	Published - Nov 19 2009
Event	2009 IEEE International Symposium on Information Theory, ISIT 2009 - Seoul, Korea, Republic of Duration: Jun 28 2009 → Jul 3 2009

Other

Other	2009 IEEE International Symposium on Information Theory, ISIT 2009
Country/Territory	Korea, Republic of
City	Seoul
Period	6/28/09 → 7/3/09

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title = "On linear balancing sets",

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 F n is called a balancing set if for every word y ε 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.",

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AB - 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 F n is called a balancing set if for every word y ε 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.

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BT - 2009 IEEE International Symposium on Information Theory, ISIT 2009

T2 - 2009 IEEE International Symposium on Information Theory, ISIT 2009

Y2 - 28 June 2009 through 3 July 2009

ER -

On linear balancing sets

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