Special Matrices over Finite Fields and Their Applications to Quantum Error-Correcting Codes

The paper investigates properties of matrix-product (MP) codes over finite fields, where the defining matrix satisfies the condition that its conjugate transpose is a (D, τ)-monomial matrix. It provides explicit formulas and necessary and sufficient conditions for such MP codes to have desirable properties like being Hermitian dual-containing, almost Hermitian dual-containing, Hermitian self-orthogonal, almost Hermitian self-orthogonal, and Hermitian LCD.