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In an earlier paper, the authors presented an algorithm for finding all polyhedral solid objects with a given set of vertices and straight line edges (its wire frame). This paper extends the Wire Frame algorithm to find all solid polyhedral objects with a given set of two dimensional projections. These projections may contain depth information in the form of dashed and solid lines, may represent cross sections, and may be overall or detail views. The choice of labeling conventions in the projections determines the difficulty of the problem. It is shown that with certain conventions and projections the problem of fleshing out projections essentially reduces to the problem of fleshing out wire frames. Even if no labeling is used, the Projections algorithm presented here finds all solutions even though it is possible to construct simple examples with a very large number of solutions. Such examples have a large amount of symmetry and various accidental coincidences which typically do not occur in objects of practical interest. Because of its generality, the algorithm can handle pathological cases if they arise. This Projections algorithm, which has applications in the conversion of engineering drawings in a Computer Aided Design, Computer Aided Manufacturing (CADCAM) system, has been implemented. The algorithm has successfully found solutions to problems that are rather complex in terms of either the number of possible solutions or the inherent complexity of projections of objects of engineering interest.

Majority-logic decoding is attractive for three reasons: (1) It can be simply implemented; (2) the decoding delay is short; and (3) its performance, while suboptimal, is always superior to bounded distance decoding. For these reasons, majority-logic decodable cyclic codes are very suitable for error control in high speed digital data transmission systems. Among the majority-logic decodable codes, the one-step decodable codes can be most easily implemented; they employ a single majority-logic gate. In this paper we study a class of one-step majority-logic decodable cyclic codes. First, we describe these codes in a simple manner. Second, a way of finding the orthogonal polynomials for decoding these codes is presented. Third, we show that for a given error correction capability, the ratio of the number of parity digits to the code length goes to zero as the code length increases. For error correction Capabilities of the form 2k - 1 or 2k, we determine the dimensions of the codes exactly.

Given a polyhedral object, its wire frame is the set of its edges and vertices. In this paper we present an algorithm which discovers all objects with a given wire frame. This algorithm, which has a number of applications to mechanical design besides being of mathematical interest, has been implemented and has performed well on complex objects.

A comparative study is made of algorithms for a general multidimensional problem involving the packing of k-part objects in k compartments in a large supply of bins. The goal is to pack the objects using a minimum number of bins. The properties and limitations of the algorithms are discussed, including k-dimensional analogs of some popular one-dimensional algorithms. An application of the algorithms is the design of computer networks.