On de Bruijn Array Codes—Part II: Pseudo-Random Array Codes

pseudo-random array is a two-dimensional array in which eachn1×n2nonzero matrix is contained exactly once as a window in the array. The pseudo-random arrays we consider have many desirable properties in addition, such as the shift-and-add-property, i.e., the addition of the array to any of its nontrivial shifts is another nontrivial shift of the array. A pseudorandom array code is a linear code ofr1×r2arrays in which eachn1×n2nonzero matrix is contained exactly once as a window in one of the arrays. In this paper, new parameters for pseudo-random arrays are presented, and their construction is generalized to pseudo-random array codes. Our constructions of pseudo-random array codes are based on the folding of sequences. Two techniques to verify whether an array or a set of arrays constructed by folding is a pseudo-random array or a pseudo-random array code, respectively, are presented. These verification techniques can also be used for VLSI testing.