A theory for planning collision-free paths of a moving object among obstacles is described. Using the concepts of state space and rotation mapping, the relationship between the positions and the corresponding collision-free orientations of a moving object among obstacles is represented as some set of a state space. This set is called the rotation mapping graph (RMG) of that object. The problem of finding collision-free paths for an object translating and rotating among obstacles is thus transformed to that of considering the connectivity of the RMG. Since the connectivity of the graph can be solved by topological methods, the problem of planning collision-free paths is easily solved in theory. Using this theory, a topological method for planning collision-free paths of a rod-object translating and rotating among obstacles is presented. If a nonrigid robotic arm is viewed as a composite rod with some degrees of freedom, the planning of collision-free paths of a robotic arm can be solved in a similar way to a rod.

This paper introduces two new edge detection algorithms. One uses multiple difference-based edge detectors. This scheme selects peak center by absolute maximum or center of mass techniques. The other algorithm is motivated by the observation that second-order enhancement improves human contour extraction, but generally confuses difference-based edge detectors. This algorithm translates intensity images into three state images (plus one, zero, and minus one), then uses multiple three-state edge masks to find edge positions. The second scheme has a multiple hardware implementation and interesting biological analogs. Finally, the two operators introduced are compared to some popular edge detection techniques from the literature.

A description of techniques used for semantic modeling in a deductive question-answering system is given. The system maintains a dialog and is able to understand situations which can be expressed as a series of sequential time-frames. Specific relevant questions are asked by the system when it is unable to succeed in a given task. It can also provide reasons for its previous actions.

This paper describes an interesting application of error correcting codes to improve the reliability of data transmission of a radio-based communication system. It shows how a low-cost system can be designed and constructed to bring significant improvements to the system's performance when a proper approach is taken to both select and implement the coding scheme.

Based on the Mattsom-Solomon polynomial, a class of algebraic linear error-correcting codes is proposed, which includes the Bose-Chaudhuri-Hocquenghen (BCH) codes, Goppa codes, and Srivastava codes as subclasses. Several constructive bounds on the minimum distance of these codes are derived and are shown to be achievable using either Berlekamp's iterative decoding algorithm or Goppa's method based on divided difference. Moreover, it is shown that this class of codes asymptotically approaches the Varshamov-Gilbert bound asn \rightarrow \infty. Although some binary Goppa codes were previously known to haven \leq 2^m, r \leq m \cdot t, andd \geq 2t+ 1, it is shown that a much larger class of codes also possesses such parameters. Finally, shortened codes are considered. With a limited computer search, a number of good codes were found. It is also observed that the proposed codes have no fundamental difference from those recently given by Helgert.

Two classes of simple low-rate burst-correcting convolutional codes that meet the Gallager bound ofg/b \geq 1 + R/1 - Rare presented. Special cases of these codes are also shown to meet the Peterson and Weldon bound ofb \leq [\frac{1}{2}(n_A -- 1)]. A third class of low-rate codes that can correct iow-density typeB2bursts is also presented. All three classes of codes are majority-logic decodable and, hence, can be easily implemented.

Some elementary mathematical properties of term matching document retrieval systems are developed. These properties are used as a basis for a new file organization technique. Some of the advantages of this new method are (1) the key-to-address transformation is easily determined; (2) the documentary information is stored only once in the file; (3) the file organization allows the use of various matching functions and thresholds; and (4) the dimensionality of the transform is easily expanded to accommodate various sized data bases.

Threshold-type retrieval functions have been suggested by many people and used widely in clustering algorithms. In this paper, a discriminating capacity is defined for these retrieval functions. Explicit methods for computation are presented. The discriminating capacity is useful as a quantitative measure for the retrieval power of each function and can serve as a guide for selection.

A new class of cyclic multiple-error-correcting arithmetic codes is described, and the minimum distance of these codes is determined analytically. A two-step majority-logic decoding scheme is developed for these arithmetic codes. The new class of codes is extended to a new class of arithmetic codes having a primitive cyclotomic factor as the generator and anL-step majority-logic decoding scheme is developed for the extended class of codes.

In many communication channels noise disturbances occur in the form of low-density bursts. Codes capable of correcting multiple bursts of low density are efficient tools of error control for such channels. One such class of codes is presented ia this paper. This Class of codes can be decoded by simple majority logic. The approach is to use codes which are the duals of product codes whose component codes are majority-logic-decodable cyclic codes.

In high-speed multipliers, multiplication is activated by processing a group of bits in parallel. As a result, any defects in circuitry produce possible errors in positions that are separated by fixed periods. A class of codes for the correction of such iterative error patterns resulting from a single fault is presented in this paper. A decoding algorithm together with a simple implementation scheme is also discussed.

A new proof has been found to establish the BCH bound, which relates the minimum distance of a cyclic code to the number of consecutive roots its generator polynomial possesses in a certain field. This new proof is recursive in nature and is very simple in structure. It makes no use of the Van der Monde determinant while it unifies the concepts of distance, estimation, and decoding.

This paper presents a number of interesting results relating to the determination of actual minimum distance of cyclic codes. Codes with multiple sets of consecutive roots are constructed. A bound on the minimum weight of odd-weight codewords is determined. Relations on the distribution of roots of the generator polynomial are investigated. Location polynomials of reversible codes are examined. These results are used to obtain better estimates of the minimum distance of many new cyclic codes.

The direct product ofpsingle parity-check codes of block lengthsn_1,n_2, \cdots ,n_pis a cyclic code of block lengthn_1 \times n_2 \times \cdots \times n_pwith(n_1 - 1) \times (n_2 - 1) \times \cdots \times (n_p - 1)information symbols per block, if the integersn_1,n_2 \cdots ,n_pare relatively prime in pairs. A lower bound for the single-burst-correction (SBC) capability of these codes is obtained. Then, a detailed analysis is made forp = 3, and it is shown that the codes can correct one long burst or two short bursts of errors. A lower bound for the double-burst-correction (DBC) capability is derived, and a simple decoding algorithm is obtained. The generalization to correcting an arbitrary number of bursts is discussed.

This paper describes a technique for high-speed decoding of burst-error-correcting codes and a class of codes most suitable for this purpose. With a small amount of additional circuitry the decoders proposed in this paper are capable of decoding speeds several orders of magnitude higher than those of conventional decoders.

Many data-transmission and data-storage systems are corrupted by disturbances of both the burst type and the random type. In this paper two classes of error-correcting codes for use with these systems have been constructed analytically and with the aid of a computer. Although not optimal, these codes do have the advantage of ease of implementation,

This paper treats the problem of automatic fault diagnosis for systems with multiple faults. The system is decomposed into n units u1, u2, . . . , un, where a unit is a well-identifiable portion of the system which cannot be further decomposed for the purpose of diagnosis. By means of a given arrangement of testing links (connection assignment) each unit of the system tests a subset of units, and a proper diagnosis can be arrived at for any diagnosable fault pattern. Methods for optimal assignments are given for instantaneous and sequential diagnosis procedures.

In this paper, methods for document retrieval are derived from algebraic coding theory. It is shown that these methods are efficient in information representation and that the amount of computation required in implementation is quite reasonable.

Linear residue codes are useful for error control in both arithmetic operations and data transmission. When used in data transmission, they do not require special coding equipment, as encoding and decoding operations may be easily carried out in digital computers. In this paper, number-theoretic concepts are used to construct linear residue codes for the correction of burst errors. A general theory is developed for the class of codes derived from the multiplicative groupG(A)moduloA, an odd integer, which consists of all the integers smaller than and relatively prime toA. Construction schemes for various classes of burst-error-correcting binary linear residue codes are determined and discussed.

This paper presents new general error-correction procedures for fhe class of codes known as Bose-Chaudhuri-Hocquenghem codes. It is shown that these procedures are efficient in time required for error-correction, and that they can be implemented with relatively simple electronic circuits. A comparison is also made with existing procedures.