In this paper, we discuss the application of byte error detecting codes to the design of self-checking circuits for the single stuck-at fault model. We discuss strongly fault-secure realization of a given Boolean function using byte error detecting codes. Even though parity is the most efficient separable code for the detection of single errors, we show that the use of a byte error detecting code can lead to lower cost of self-checking realization of a given function as compared to its self-checking realization using the parity code. We also present a method for the design of totally self-checking checkers for byte error detecting codes. Experimental results obtained for various test circuits are also discussed.