2019/01/09 by Mahdi Cheraghchi, Cheraghchi, Mahdi, João Ribeiro +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #Advanced biosensing and bioanalysis techniques #FOS: Computer and information sciences #Information Theory (cs.IT) #Privacy-Preserving Technologies in Data #SARS-CoV-2 detection and testing
paper · pdf · doi:10.48550/arxiv.1901.02852
openalex publication_date 2019/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Construction of error-correcting codes achieving a designated minimum distance parameter is a central problem in coding theory. In this work, we study a very simple construction of binary linear codes that correct a given number of errors K. Moreover, we design a simple, nearly optimal syndrome decoder for the code as well. The running time of the decoder is only logarithmic in the block length of the code, and nearly linear in the number of errors K. This decoder can be applied to exact for-all sparse recovery over any field, improving upon previous results with the same number of measurements. Furthermore, computation of the syndrome from a received word can be done in nearly linear time in the block length. We also demonstrate an application of these techniques in non-adaptive group testing, and construct simple explicit measurement schemes with O(K2 log2 N) tests and O(K3 log2 N) recovery time for identifying up to K defectives in a population of size N.