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2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2005)
Pittsburgh, Pennsylvania, USA
Oct. 23, 2005 to Oct. 25, 2005
ISBN: 0-7695-2468-0
pp: 317-326
Tali Kaufman , School of Computer Science, Tel Aviv University
Simon Litsyn , Department of Electrical Engineering-Systems,Tel Aviv University
<p>A code is said to be locally testable if an algorithm can distinguish between a codeword and a vector being essentially far from the code using a number of queries that is independent of the code?s length. The question of characterizing codes that are locally testable is highly complex. In this work we provide a sufficient condition for linear codes to be locally testable. Our condition is based on the weight distribution (spectrum) of the code and of its dual. </p> <p>Codes of (large) length n and minimum distance \frac{n}{2} - \Theta (\sqrt n ) have size which is at most polynomial in n. We call such codes almost-orthogonal. We use our condition to show that almost-orthogonal codes are locally testable, and, moreover, their dual codes can be spanned by words of constant weights (weight of a codeword refers to the number of its non-zero coordinates).</p>
Tali Kaufman, Simon Litsyn, "Almost Orthogonal Linear Codes are Locally Testable", 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, vol. 00, no. , pp. 317-326, 2005, doi:10.1109/SFCS.2005.16
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