This paper presents a method for constructing quantum error-correcting codes by transforming the problem into finding additive codes over the finite field GF(4) that are self-orthogonal with respect to a trace inner product. The authors introduce a framework that connects quantum error correction with classical coding theory, allowing the use of known results from classical coding theory to construct quantum codes. They show that quantum error-correcting codes can be represented as additive codes over GF(4), and that self-orthogonal additive codes over GF(4) correspond to quantum codes with certain parameters. The paper also discusses various constructions of quantum codes, including direct sums, puncturing, shortening, and concatenation, and provides bounds on the parameters of such codes. The authors also explore the relationship between quantum codes and classical codes, and present several examples of quantum codes, including the [[25,1,9]] code derived from the [[5,1,3]] Hamming code. The paper concludes with a discussion of the properties of additive codes and their applications in quantum error correction.This paper presents a method for constructing quantum error-correcting codes by transforming the problem into finding additive codes over the finite field GF(4) that are self-orthogonal with respect to a trace inner product. The authors introduce a framework that connects quantum error correction with classical coding theory, allowing the use of known results from classical coding theory to construct quantum codes. They show that quantum error-correcting codes can be represented as additive codes over GF(4), and that self-orthogonal additive codes over GF(4) correspond to quantum codes with certain parameters. The paper also discusses various constructions of quantum codes, including direct sums, puncturing, shortening, and concatenation, and provides bounds on the parameters of such codes. The authors also explore the relationship between quantum codes and classical codes, and present several examples of quantum codes, including the [[25,1,9]] code derived from the [[5,1,3]] Hamming code. The paper concludes with a discussion of the properties of additive codes and their applications in quantum error correction.