$c^3$-Locally Testable Codes from Lossless Expanders

TL;DR

This paper introduces a new family of locally testable codes constructed using lossless expanders and balanced products, addressing a key open problem in coding theory.

Contribution

It presents the first construction of $c^3$-LTCs with constant rate, distance, and locality using lossless expanders and balanced products.

Findings

Constructed $c^3$-LTCs with desired properties

Utilized 1-sided lossless expanders and balanced products

Advances understanding of LTCs with optimal parameters

Abstract

A locally testable code (LTC) is an error correcting code with a property tester. The tester tests if a word is codeword by reading constant random bits and rejects the word with probability proportional to the distance from the word to the closest codeword. An important open question until recently is whether there exist $c^3$-LTCs which are LTCs with constant rate, constant relative distance and constant locality. In this work, we construct a new LTC family using 1-sided lossless expanders and balanced products.