@inproceedings{e22a7ecb9b5045629e9258073fc89dd6,
title = "Matching vector codes",
abstract = "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.",
keywords = "Locally decodable codes, Matching vectors, Reed Muller codes",
author = "Zeev Dvir and Parikshit Gopalan and Sergey Yekhanin",
year = "2010",
doi = "10.1109/FOCS.2010.73",
language = "English (US)",
isbn = "9780769542447",
series = "Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS",
publisher = "IEEE Computer Society",
pages = "705--714",
booktitle = "Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010",
address = "United States",
note = "2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010 ; Conference date: 23-10-2010 Through 26-10-2010",
}