New quantum codes from constacyclic codes over a non-chain ring

Let p be a prime of the form p = m t + 1 , where integers t ≥ 1 , m ≥ 2 and R m = F p [ u ] / ⟨ u m - 1 ⟩ . Thus, R m is a finite commutative non-chain ring. For a given unit λ ∈ R m , we study λ -constacyclic codes of length n over R m . The necessary and sufficient conditions for these codes to contain their Euclidean duals are determined. As an application from dual-containing λ -constacyclic codes over R m , for m = 2 , 3 , 4 , we obtain many new quantum codes that improve on the known existing quantum codes.