LCP of λ-constacyclic codes over finite chain rings (Coding Theory)

Let R be a finite commutative chain ring with unity and be a unit in R. In this paper, all non-trivial linear complementary pair (LCP) of λ-constacyclic codes of arbitrary length over R have been completely determined. An expression for the total number of non-trivial LCP of λ-constacyclic codes of length n over R has also been derived in terms of the maximum number of factors of xn λ into monic, pairwise coprime polynomials of degree greater than or equal to 1 over R. Further, using the algebraic structure of λ-constacyclic codes over finite chain rings of nilpotency index 2 as an alternative approach, the complete characterization of non-trivial LCP of λ-constacyclic codes is obtained for such rings. As an illustration of our results, a few examples of non-trivial LCP of constacyclic codes over the rings Z8, Z4 and the Galois ring GR(4, 3) have been given.

DOI: 10.1007/s12190-022-01816-w