M-Array Based on Non-Zero Maps

Two-dimensional maximum area array (m-array) is a typical pseudo-random array with specific window property - all sub-windows are globally unique. M-array constructed by Formula-Method-Based encoding algorithm features a big difference between the number of rows and columns. Enumeration-Method-Based encoding algorithm only constructs small-size m-array with high computational complexity and low success rate. Based on the characteristics of Galois Fields, a new method of m-array construction based on non-zero maps theory is proposed and the theoretical proof is presented. Given symbols p and sub-window size m×n as input, m-array with a large array size and close numbers of rows and columns is constructed by dividing and splicing m-sequence. Comparing with existing methods, the advantages of the algorithm include larger array size, more balanced number of rows and columns, and lower computational complexity. If needed, the method in this paper is flexible enough that the number of rows and columns of m-array can also be adjusted within a certain range, meaning that m-array with specific rows and columns ratio can be constructed.