Most of quantum codes have been constructed by using classical linear codes over finite field. However, little is known about the construction of quantum codes via group character codes. In this work, we present the constructions of nonbinary quantum and asymmetric quantum codes based on group character codes, and give explicit parameters for infinite families of nonbinary quantum codes and asymmetric quantum codes. Furthermore, we present families of optimal quantum codes which derived from group character codes.
Generalizing the linear complementary duals, the linear complementary pairs and the hull of codes, we introduce the concept of
ℓ-dimension linear intersection pairs (
ℓ-DLIPs) of codes over a finite commutative ring
(R), for some positive integer
ℓ. In this paper, we study
ℓ-DLIP of codes over
R in a very general setting by a uniform method. Besides, we provide a necessary and sufficient condition for the existence of a non-free (or free)
ℓ-DLIP of codes over a finite commutative Frobenius ring. In addition, we obtain a generator set of the intersection of two constacyclic codes over a finite chain ring, which helps us to get an important characterization of
ℓ-DLIP of constacyclic codes. Finally, the
ℓ-DLIP of constacyclic codes over a finite chain ring are used to construct new entanglement-assisted quantum error correcting (EAQEC) codes.