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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", FOCS, 2005, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, 2013 IEEE 54th Annual Symposium on Foundations of Computer Science 2005, pp. 317-326, doi:10.1109/SFCS.2005.16
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