Linear complementary pairs of constacyclic n-D codes over a finite commutative ring

In this paper, a necessary condition which is sufficient as well for a pair of constacyclic 2-D codes over a finite commutative ring R to be an LCP of codes has been obtained. Also, a characterization of non-trivial LCP of constacyclic 2-D codes over R has been given and total number of such codes has been determined. The above results on constacyclic 2-D codes have been extended to constacyclic 3-D codes over R. The obtained results readily extend to constacyclic n-D codes, \(n \ge 3\) $n\ge 3$ , over finite commutative rings. Furthermore, some results on existence of non-trivial LCP of constacyclic 2-D codes over a finite chain ring have been obtained in terms of its residue field.