Local-Testability and Self-Correctability of q-ary Sparse Linear Codes
Computational Complexity
2015-03-17 v1 Information Theory
math.IT
Abstract
We prove that q-ary sparse codes with small bias are self-correctable and locally testable. We generalize a result of Kaufman and Sudan that proves the local testability and correctability of binary sparse codes with small bias. We use properties of q-ary Krawtchouk polynomials and the McWilliams identity -that relates the weight distribution of a code to the weight distribution of its dual- to derive bounds on the error probability of the randomized tester and self-corrector we are analyzing.
Keywords
Cite
@article{arxiv.1012.3506,
title = {Local-Testability and Self-Correctability of q-ary Sparse Linear Codes},
author = {Widad Machmouchi},
journal= {arXiv preprint arXiv:1012.3506},
year = {2015}
}