High-rate codes with sublinear-time decoding
Proceedings of the forty-third annual ACM symposium on Theory of computing
Locally decodable codes: a brief survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Three-Query Locally Decodable Codes with Higher Correctness Require Exponential Length
ACM Transactions on Computation Theory (TOCT)
SIAM Journal on Computing
A novel elementary construction of matching vectors
Information Processing Letters
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A locally decodable code encodes a message by a codeword, such that even if the codeword is corrupted by noise, each message bit can be recovered with high probability by a randomized decoding procedure that reads only few bits of the codeword. Recently a new class of locally decodable codes, based on families of vectors with restricted dot products has been discovered. We refer to those codes as Matching Vector (MV) codes. In this work we develop a new view of MV codes and uncover certain similarities between them and classical Reed Muller codes. Our view allows us to obtain a deeper insight into the power and limitations of MV codes. We use it to construct codes that can tolerate more errors or are shorter than previously known codes for certain parameter settings. We also show super-linear lower bounds on the codeword length of any MV code.