In modern age, the increasing complexity of computation and communication technology is leading us towards the necessity of new paradigm. As a result, unconventional approach like DNA coding theory is gaining considerable attention. The storage capacity, information processing and transmission properties of DNA molecules stimulate the notion of DNA coding theory as well as DNA cryptography. In this paper we generate DNA codeword using DNA linear block codes which ensures the secure transmission of information. In the proposed code design strategy DNA-based XOR operation (DNAX) is applied for effective construction of DNA codewords which are quadruples generated over the set of alphabets consisting of four DNA bases adenine, thymine, guanine, and cytosine. By worked out examples we explain the use of generator matrix and parity check matrix in encryption and decryption of coded data in the form of short single stranded DNA sequences. The newly developed technique can detect as well as correcting error in transmission of DNA codewords through biological channels from sender to the intended receiver. Through DNA coding theory we are expanding the paths towards data compression and error correction in the form of DNA strands. This leads us towards a broader domain of DNA cryptography.