ABSTRACT
We have shown that orthogonal arrays (OA) of index unity can be used to construct perfect Cartesian codes (Theorem 3.2). Several known constructions of orthogonal arrays of index unity will be described in this chapter. Section 7.1 presents the construction of orthogonal arrays with strength 2 by using an affine plane over finite fields and orthogonal Latin squares. Sections 7.2 and 7.3 are devoted to the proof of the existence of OA(n2, 4, n, 2) for any positive integers n except n = 2, 6, which is equivalent to the existence of orthogonal Latin squares of order n = 2, 6. Section 7.4 describes the constructions due to Bush [7]. Section 7.5 explores the connections between orthogonal arrays and error-correcting codes. It is shown in Section 7.6 that all maximal distance separable (MDS) codes are equivalent to orthogonal arrays of index unity. The construction using Reed-Solomon codes, which are MDS codes, is described in this section.
