Some New Results on Pseudo-random Arrays

Abstract

Arrays whose two-dimensional auto-correlation functions have desirable correlation properties have found applications in spectrometry, acoustics, and cryptography for encrypting two-dimensional arrays such as images. As pointed out by I.M. Chakravarti, Gates, and Azais, such arrays are applicable in the design of experiments where a plant competes with neighbors of the same type and a second type. This talk will deal with some new constructions of such arrays. We shall call them: perfect arrays. Several new families of these have been constructed by the speaker (joint work with Warwick de Launey in the quaternary case, with John Dillon and Kevin Player in the binary/ternary case). There are certain variations of these in the literature. We shall give a brief overview of this subject matter. The exciting news is that we are settling a few recent conjectures of Lin and Gong on perfect ternary sequences.