On the \(\ell\)-DLIPs of codes over finite commutative rings (Q6197721)

The article under review introduces the concept of \(\ell\)-dimension linear intersection pairs (\(\ell\)-DLIPs) of codes over a finite commutative ring \(R\). This is a generalization of the concept of \(\ell\)-linear intersection pairs (\(\ell\)-LIPs), which have been widely studied for applications in cryptography and quantum error-correction. The authors find several characterizations for \(\ell\)-DLIPs of codes over finite commutative Frobenius rings. As a consequence, this also gives conditions for having linear complementary pairs (LCPs) of codes, and for having a code with \(\ell\)-dimensional hull. These results are then applied to the particular case of constacyclic codes, where the authors find characterizations for LCPs of constatyclic codes and they construct entanglement-assisted quantum error-correcting (EAQEC) codes.