On the Modulus in Matching Vector Codes
Lin Zhu, Wen Ming Li, Liang Feng Zhang

TL;DR
This paper investigates the properties of good moduli in matching vector codes, demonstrating the existence of infinitely many such numbers and providing methods to generate smaller good numbers with the same prime divisors.
Contribution
It extends the understanding of good moduli in MVCs by proving the existence of infinitely many good numbers and offering explicit construction methods.
Findings
Good numbers of the form p1^α1 p2^α2 are characterized.
Multiples of good numbers of the same form are also good.
Infinitely many new good numbers can be constructed explicitly.
Abstract
A -query locally decodable code (LDC) allows one to encode any -symbol message as a codeword of symbols such that each symbol of can be recovered by looking at symbols of , even if a constant fraction of have been corrupted. Currently, the best known LDCs are matching vector codes (MVCs). A modulus may result in an MVC with and . The is {\em good} if it is possible to have . The good numbers yield more efficient MVCs. Prior to this work, there are only {\em finitely many} good numbers. All of them were obtained via computer search and have the form . In this paper, we study good numbers of the form . We show that if is good, then any…
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Taxonomy
TopicsCoding theory and cryptography · DNA and Biological Computing · Cooperative Communication and Network Coding
