A Method for Constructing Circuit Codes

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Abstract
A d -dimensional circuit code of spread s (also called SIB s , code or circuit code of minimum distance s ) is a simple circuit Q in the graph of the d -dimensional cube [0, 1] d such that any two vertices of Q differing in exactly r coordinates, with r < s , can be joined by a path formed from r edges of Q . Such codes are designed to introduce error detection into certain analog-to-digital conversion systems. Longer codes correspond to increased accuracy of the system, and hence there is interest in determining the maximum length C ( d , s ) of d -dimensional circuit codes of spread s . In the present study the author contributes to this problem for even values of s by describing a method of combining a code of spread s with a suitably related code of spread s -1 so as to produce a longer code of spread s .

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