Abstract
We continue the study of robust tensor codes and expand the class of base codes that can be used as a starting point for the construction of locally testable codes via robust two-wise tensor products. In particular, we show that all unique-neighbor expander codes and all locally correctable codes, when tensored with any other good-distance code, are robust and hence can be used to construct locally testable codes. Previous works by [2] required stronger expansion properties to obtain locally testable codes.
Our proofs follow by defining the notion of weakly smooth codes that generalize the smooth codes of [2]. We show that weakly smooth codes are sufficient for constructing robust tensor codes. Using the weaker definition, we are able to expand the family of base codes to include the aforementioned ones.
Research supported in part by a European Community International Reintegration Grant, an Alon Fellowship, and grants by the Israeli Science Foundation (grant number 679/06) and by the US-Israel Binational Science Foundation (grant number 2006104).
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Ben-Sasson, E., Viderman, M. (2008). Tensor Products of Weakly Smooth Codes Are Robust. In: Goel, A., Jansen, K., Rolim, J.D.P., Rubinfeld, R. (eds) Approximation, Randomization and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2008 2008. Lecture Notes in Computer Science, vol 5171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85363-3_24
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DOI: https://doi.org/10.1007/978-3-540-85363-3_24
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