Perfect Bit Fields and Their Technical Application

By a Perfect Bit Field (PBF) we understand a 2-dimensional binary array in which each possible binary subarray of fixed dimensions appears exactly once. The topic of PBFs is closely connected to the theme of de Bruijn sequences which are 1-dimensional analogies of PBFs. Unlike de Bruijn sequences the construction of non-trivial PBFs is relatively difficult and technically rather demanding. The topic of PBFs appears from time to time but there is no systematic approach and overall theory available. We provide a short survey of available techniques and present our own results aimed at the practice of PBFs generation. We also present a possible industry application of PBFs. The application consists in the exact position location of a soil excavator bucket by means of a camera system. The aim is to provide feedback between the excavator bucket target and real position during the excavator tests with the loaded bucket.