Multimodal biometric systems provide a way to combat with the limitations of a unimodal biometric system which include less accuracy and user acceptability. In this context, a coding based approach called bit-transition code, is proposed for addressing the less-explored problem of designing a biometric-based authentication system by combining the iris and palmprint modalities. The approach is based on the encoding of binary transitions of symmetric and asymmetric parts of the Gabor filtered images at all pixel locations. Score-level fusion is employed to integrate the individual iris and palmprint performances. Experiments are carried out with three benchmark iris/palmprint databases, namely IITD iris and palmprint databases and PolyU palmprint database. The performance is measured in terms of receiver operator characteristics (ROC) curves and other metrics, like equal error rate and area under ROC curves. A comprehensive comparison, with several state-of-the-art approaches, is presented in order to validate the usefulness of the proposed approach.