This correspondence considers three-level AND/OR gate realizations for T or more of N symmetric functions and gives a design procedure. The procedure can be used to design relatively large networks. The three-level realizations require substantially fewer test patterns for fault detection, gates, and gate inputs than the minimum two-level network. For example, the minimum two-level network for the 3 or more out of 12 functions requires 286 test patterns, 67 gates, and 726 gate inputs while the three-level realization presented requires 27 test patterns, 25 gates, and 96 gate inputs.

A bound and construction are presented for high-rate burst-error-correcting recurrent codes. The bound is an upper bound on the block length in terms of the total redundancy used in decoding, the redundancy per block, and the burst length. The construction uses a block-code parity-check matrix as the first block of the recurrent code parity-check matrix. For a block code it is typical to find that only a portion of the redundancy need be used to detect a burst. Any block code for which this is true can be used in the construction. The recurrent code is then related as follows to the block code from which it is constructed. 1) The recurrent code block length is the same as the block-code block length. 2) The total redundancy used in decoding the recurrent code is the same as the block-code redundancy per block. 3) The recurrent code redundancy per block is the same as the block-code redundancy required for burst detection only. 4) The recurrent code is of higher rate than the block code. 5) The recurrent code requires a guard space between bursts but otherwise corrects the same bursts as the block code. It is shown that, when certain well-known cyclic codes are used in the construction, the resulting recurrent codes are close to the upper bound.

It is shown that there exists a large class of cyclic codes for which there are circulant bases.