We introduce a new class of real number codes derived from DFT matrix, Hermitian symmetric DFT (HSDFT) codes. We propose a new decoding algorithm based on coding-theoretic as well as subspace based approach. Decoding of HSDFT codes requires only real arithmetic operations and smaller dimension matrices compared to the decoding of the state-of-art real BCH DFT (RBDFT) class of codes. HSDFT codes will also be shown to have more burst error correction capacity. For a Gauss-Markov source, on a binary symmetric channel at lower to moderate bit error rates (BERs), HSDFT codes show better performance than RBDFT codes, and on a Gilbert-Elliot channel HSDFT codes consistently perform better than RBDFT codes.