On Separable Unordered Codes

Unordered codes have proven useful for designing failsafe, fault-secure, and self-checking logic circuits. In many applications it may be desirable to have separate information bits and check bits, i.e., a separable code. This correspondence gives a procedure for adding check bits to a set of information k-tuples to produce an unordered code. The general case where not all 2^k possible k-tuples are used is considered. For an arbitrary set of k-tuples, the minimum number of check bits is shown.