Simple Codes and Sparse Recovery with Fast Decoding

Construction of error-correcting codes achieving a designated minimum distance parameter is central problem in coding theory. In this work, we study very simple construction binary linear that correct given number errors . Moreover, design simple, nearly optimal syndrome decoder for the code as well. The running time only logarithmic block length and This can be applied to exact for-all sparse recovery over any field, improving upon previous results with same measurements. Furthermore, computation from received word done length. We also demonstrate an application these techniques nonadaptive group testing construct explicit measurement schemes tests identifying up defectives population size