Error-correcting codes over the real field are studied which can locate outlying computational errors when performing approximate computing of real vector--matrix multiplication on resistive crossbars. Prior work has concentrated on locating a single outlying error and, in this work, several classes of codes are presented which can handle multiple errors. It is first shown that one of the known constructions, which is based on spherical codes, can in fact handle multiple outlying errors. A second family of codes is then presented with $\zeroone$~parity-check matrices which are sparse and disjunct; such matrices have been used in other applications as well, especially in combinatorial group testing. In addition, a certain class of the codes that are obtained through this construction is shown to be efficiently decodable. As part of the study of sparse disjunct matrices, this work also contains improved lower and upper bounds on the maximum Hamming weight of the rows in such matrices.

翻译：研究了实数域上的纠错码，这些码能在电阻交叉阵列上进行实向量-矩阵乘法的近似计算时定位异常计算误差。此前的工作集中于定位单个异常误差，而本文提出了几类可处理多重误差的编码方案。首先证明，基于球面编码的已知构造实际上能够处理多重异常误差。随后提出第二类编码，其校验矩阵为稀疏且分离的零一矩阵；此类矩阵已在其他应用（尤其是组合群组测试）中得到广泛使用。此外，通过该构造获得的某类编码被证明可高效解码。作为稀疏分离矩阵研究的组成部分，本文还改进了此类矩阵行最大汉明重量的上下界。