One of the central problems in coding theory is to construct codes with best possible parameters and properties. A special class of codes called quasi-twisted (QT) codes is well-known to produce codes with good parameters. Most of the work on QT codes has been over the 1-generator case. In this work, we focus on 2-generator QT codes and generalize the ASR algorithm that has been very effective to produce new linear codes from 1-generator QT codes. As a result of implementing the generalized algorithm, we have found 103 2-generator QT codes that are new among the class of QT codes. Additionally, most of these codes possess the following additional properties: a) they have the same parameters as best known linear codes, and b) many of them have additional desired properties such as being LCD and dual-containing. Further, we have also found a binary 2-generator QT code that is new (record breaking) among all binary linear codes [I] and its extension yields another record breaking binary linear code.

In this paper, we study Z2Z4-additive cyclic codes. These codes are identified as Z4[x]-submodules of the ring Rr,s=Z2[x]/〈xr-1〉×Z4[x]/〈xs-1〉. The algebraic structure of this family of codes is studied and a set of generator polynomials for this family as a Z4[x]-submodule of the ring Rr,sis determined. We show that the duals of Z2Z4-additive cyclic codes are also cyclic. We also present an infinite family of Maximum Distance separable with respect to the singleton bound codes. Finally, we obtain a number of binary linear codes with optimal parameters from the Z2Z4-additive cyclic codes.

In this paper, we study a special type of quasi-cyclic (QC) codes called skew QC codes. This set of codes is constructed using a noncommutative ring called the skew polynomial ringF[x;¿]. After a brief description of the skew polynomial ringF[x;¿], it is shown that skew QC codes are left submodules of the ringRsl=(F[x;¿]/(xs-1) )l. The notions of generator and parity-check polynomials are given. We also introduce the notion of similar polynomials in the ringF[x;¿] and show that parity-check polynomials for skew QC codes are unique up to similarity. Our search results lead to the construction of several new codes with Hamming distances exceeding the Hamming distances of the previously best known linear codes with comparable parameters.

One of the most important and challenging problems in coding theory is to construct codes with the best possible parameters. Quasi-cyclic (QC) and the larger class of quasi- twisted (QT) codes have been proven to contain many good codes (with best-known parameters). In this paper, we review some open problems concerning these codes, introduce generalizations of QT codes, and suggest some constructions involving QT codes. We also present some new and good quaternary codes.

Knowledge has proven to be a useful and fundamental formalism for reasoning about distributed systems. The application of this formalism, however entails a loss of volition on the part of processes about which something is known. This loss of volition is often not appropriate in loosely coupled distributed systems. In this paper we generalize the formal characterization of knowledge into one of belief. Belief has the advantage of allowing processes to maintain volition. We examine some of the similarities and surprising differences between knowledge and belief. We also present some examples of distributed applications that are more conveniently characterized with belief rather than knowledge.

Previously, (linear) codes over Z/sub 4/ and quasi-cyclic (QC) codes (over fields) have been shown to yield useful results in coding theory. Combining these two ideas we study Z/sub 4/-QC codes and obtain new binary codes using the usual Gray map. Among the new codes, the lift of the famous Golay code to Z/sub 4/ produces a new binary code, a (92, 2/sup 24/, 28)-code, which is the best among all binary codes (linear or nonlinear). Moreover, we characterize cyclic codes corresponding to free modules in terms of their generator polynomials.

One of the most important problems of coding theory is to construct codes with best possible minimum distances. In this article, using the structure of quasi-cyclic (QC) codes with a BCH-type bound given by Lally and Fitzpatrick (see WCC '99, Workshop on Coding and Cryptography, Paris, France, 1999), we have found 20 new ternary quasi-cyclic codes with improved minimum distances.