A query efficient non‐adaptive long code test with perfect completeness1. Issue 4 (3rd May 2014)

• Record Type: Journal Article
• Authors: Tamaki, Suguru; Yoshida, Yuichi
• Is Part Of: Random structures & algorithms. Volume 45:Issue 4(2014)
• Page Start: 703
• Page End: 723
• Publication Date: 2014-05-03
• Subjects: Random graphs -- Periodicals; Mathematical analysis -- Periodicals; 519
• DOI: 10.1002/rsa.20549
• Languages: English
• ISSNs: 1042-9832

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>Long Code testing is a fundamental problem in the area of property testing and hardness of approximation. In this paper, we study how small the soundness <italic>s</italic> of the Long Code test with perfect completeness can be by using non‐adaptive <italic>q</italic> queries. We show that <italic>s</italic> = (2<italic>q</italic> + 3)/2^{<italic>q</italic>} is possible, where <italic>q</italic> is of the form <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh21k9v7kh" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" altimg="urn:x-wiley::media:rsa20549:rsa20549-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mn>2</mml:mn><mml:mi>k</mml:mi></mml:msup><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math></alternatives></inline-formula> for any integer <italic>k</italic> &gt; 2. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 703–723, 2014</p> </abstract>