Matching-Vector Families and LDCs Over Large Modulo
Zeev Dvir, Guangda Hu

TL;DR
This paper establishes new upper bounds on the size of Matching-Vector families over large moduli, impacting the understanding of locally decodable codes and their efficiency limits.
Contribution
It provides improved bounds on the size of Matching-Vector families for large moduli, refining previous results and implications for code length in locally decodable codes.
Findings
Bound of t ≤ O(m^{n/2+8.47}) for Matching-Vector families
Matching-Vector codes have minimum encoding length at least K^{19/18}
Improves previous super linear bounds on code length
Abstract
We prove new upper bounds on the size of families of vectors in with restricted modular inner products, when is a large integer. More formally, if and satisfy and for all , we prove that . This improves a recent bound of by \cite{BDL13} and is the best possible up to the constant 8.47 when is sufficiently larger than . The maximal size of such families, called `Matching-Vector families', shows up in recent constructions of locally decodable error correcting codes (LDCs) and determines the rate of the code. Using our result we are able to show that these codes, called Matching-Vector codes, must have encoding length…
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Taxonomy
TopicsCooperative Communication and Network Coding · Coding theory and cryptography · Interconnection Networks and Systems
