Abstract

The reconstruction of an object of a given class by its intersection with some (so-called testing) set is studied. For the class, we consider Preparata-like codes, i.e., nonlinear codes of length \( n=2^{2m}-1 \), \( m=2,3,\dots \), with code distance 5 and twice the size of a linear code of the same length and distance. Conditions are determined under which the union of a few concentric spheres forms a testing set for Preparata-like codes.

中文翻译：

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类似 Preparata 的代码的测试集

摘要

研究了通过给定类的对象与某些（所谓的测试）集的交集来重建该对象。对于该类，我们考虑类似 Preparata 的代码，即长度为 \( n=2^{2m}-1 \)、 \( m=2,3,\dots \)的非线性代码，代码距离为 5 和两倍相同长度和距离的线性代码的大小。确定几个同心球体的联合形成类似 Preparata 代码的测试集的条件。