Superquadratic Lower Bound for 3-Query Locally Correctable Codes over the Reals

THEORY OF COMPUTING, pp. 1-36, 2017.

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Abstract:

We prove that 3-query linear locally correctable codes of dimension d over the reals require block length n > d(2+)alpha some fixed, positive alpha>0. Geometrically, this means that if n vectors in R-d are such that each vector is spanned by a linear number of disjoint triples of others, then it must be that n > d(2+alpha). This improves ...More

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