This paper presents an information hiding method for DNA steganography with which a massive amount of data can be hidden in a noncoding strand. Our method maps the encrypted data to the DNA sequence using a numerical mapping table, before concealing it in the noncoding sequence using a secret key comprising sector length and the random number generator's seed. Our encoding algorithm is sector-based and reference dependent. Using modular arithmetic, we created a unique binary-base translation for every sector. By conducting a simulation study, we showed that our method could preserve amino acid information, extract hidden data without reference to the host DNA sequence, and detect the position of mutation error. Experimental results verified that our method produced higher data capacity than conventional methods, with a bpn (bit-per-nucleotide) value that ranged from approximately 1-2, depending on the selected sector length. Additionally, our novel method detected the positions of mutation errors by the presence of a parity base in each sector.