Based on the concept of an access matrix, a new protection system that achieves access control is proposed. In this system, associated with each accessor is only a key, and associated with each resource is only a lock, and through simple operations on the keys and locks, privacy decisions of the protection system can be revealed. Amechanism that realizes this system is also described. Noticing the importance of the role hierarchies play in access control, another mechanism is devised such that each node in the hierarchy is assigned a key and a simple operation on any two keys reveals the relationship of the two nodes corresponding to the two keys.

Generalized minimum distance decoding schemes are found for majority logic decodable codes. These decoding schemes are parallel to the classical majority logic decoding schemes and thus can be easily implemented.

A reformulation of MacWilliams type of relation between the split-weight enumerators of a pair of dual codes is shown to exhibit an identity on the row weight and column weight distributions of a matrix.

The error-correctiog capability of algebraic analog decoding is found when the decoding region is extended to a hypercone-like region which contains the original decoding sphere. In addition, an analogy between algebraic analog decoding and generalized minimum distance decoding is established; both are quasi-soft decision algorithms.

An optimal soft decision (maximum likelihood) decoding scheme for linear block codes is described which works in the code domain and is relatively simple. It can be simplified further by considering more channel measurement information. Furthermore, optimal decoder complexity can be traded for asymptotically optimum performance.

Two modifications of the basic correlation decoding approach are presented. One of them yields a nonexhaustive optimum word decoding algorithm whose complexity depends upon the "projecting" structure of the code. This algorithm is then modified to yield a second decoding algorithm which, while not optimum, has simpler complexity. Applications to the AWGN channel are discussed and performance curves are given for (24, 12) and (31, 15) codes.

Bit-by-bit soft-decision decoding of binary cyclic codes is considered. A significant reduction in decoder complexity can be achieved by requiring only that the decoder correct all analog error patterns which fall within a Euclidean sphere whose radius is equal to half the minimum Euclidean distance of the code. Such a "maximum-radius" scheme is asymptotically optimum for the additive white Gaussian noise (AWGN) channel. An iterative extension of the basic algebraic analog decoding scheme is discussed, and performance curves are given for the (17,9), (21,11), and (73,45) codes on the AWGN channel.

A new upper bound on the minimum distance of binary cyclic arithmetic codes of composite length is derived. New classes of binary cyclic arithmetic codes of composite length are introduced. The error correction capability of these codes is discussed, and in some cases the actual minimum distance is found. Decoding algorithms based on majority-logic decision are proposed for these codes.

In this paper we investigate the weight structure of cyclic codes of composite lengthn = n_{1} n_{2}. The actual minimum distances of some classes of binary cyclic codes of composite length are derived. For other classes, new lower bounds on the minimum distance are obtained. These new lower bounds improve on the BCH bound for a considerable number of binary cyclic codes.