Abstract
In this paper, two-dimensional arrays of elements of an arbitrary finite field are examined, especially arrays having maximum-area matrices. We first define two-dimensional linear recurring arrays. In order to study the characteristics of two-dimensional linear recurring arrays, we also define two-dimensional linear cyclic codes. A systematic method of constructing two-dimensional linear recurring arrays having maximum-area matrices is given using the theory of two-dimensional cyclic codes. These arrays, here called \gamma \beta -arrays, may be said to be two-dimensional analogs of M -sequences. A \gamma \beta -array of area N_x \times N_y exists over GF(q) if and only if N_x N_y is equal to q^N _ 1 for some positive integer N . Many interesting characteristics of the \gamma \beta -array, such as the properties of its autocorrelation function and the properties of the characteristic arrays, are deduced and explained.
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