Roberta Evans Sabin

Metacyclic error-correcting codes

Error-correcting codes which are ideals in group rings where the underlying group is metacyclic and non-abelian are examined. Such a groupG(M, N,R) is the extension of a finite cyclic group ℤM by a finite cyclic group ℤN and has a presentation of the form (S, T:SM=1,TN=1, T· S=SR·T) where gcd(M, R)=1, RN=1 modM, R ≠ 1. Group rings that are semi-simple, i.e., where the characteristic of the field does not divide the order of the group, are considered. In all cases, the field of the group ring is of characteristic 2, and the order ofG is odd.Algebraic analysis of the structure of the group ring yields a unique direct sum decomposition ofFG(M, N, R) to minimal two-sided ideals (central codes). In every case, such codes are found to be combinatorically equivalent to abelian codes and of minimum distance that is not particularly desirable. Certain minimal central codes decompose to a direct sum ofN minimal left ideals (left codes). This direct sum is not unique. A technique to vary the decomposition is described. p]Metacyclic codes that are one-sided ideals were found to display higher minimum distances than abelian codes of comparable length and dimension. In several cases, codes were found which have minimum distances equal to that of the best known linear block codes of the same length and dimension.

On minimum distance bounds for abelian codes

This paper is an exposition of two methods of formulating a lower bound for the minimum distance of a code which is an ideal in an abelian group ring. The first, a generalization of the cyclic BCH (Bose-Chaudhuri-Hoquenghem) bound, was proposed by Camion [2]. The second method, presented by Jensen [4], allows the application of the BCH bound or any of its improvements by viewing an abelian code as a direct sum of concatenations of cyclic codes. This second method avoids the mathematical analysis required for a direct generalization of a cyclic bound to the abelian case. It can produce a lower bound that improves the generalized BCH bound. We present simple algorithms for 1) deriving the generalized BCH bound for an abelian code 2) determining direct sum decompositions of an abelian code to concatenated codes and 3) deriving a bound on an abelian code, viewed as a direct sum of concatenated codes, by applying the cyclic BCH bound to the inner and outer code of each concatenation. Finally, we point out the applicability of these methods to codes that are not ideals in abelian group rings.

Impact of the Insertion of Modern Information and Communication Technologies in Brazilian Rural Communities

Information and communication technologies have the potential to overcome age-old barriers of space, time, class, and custom to integrate poor, isolated and disenfranchised rural populations into the mainstream of the larger society. This article describes Gems of the Earth, a rural community telecenter project currently in development in a poor, but once prosperous, region of Brazil. The study analyzes the impact of the telecenters on the lives of these communities. Preliminary results point to the creation of new habits and customs, with initial signs of a return to sustainable development

On row-cyclic codes with algebraic structure

In this article, some row-cyclic error-correcting codes are shown to be ideals in group rings in which the underlying group is metacyclic. For a given underlying group, several nonequivalent codes with this structure may be generated. Each is related to a cyclic code generated in response, to the metrics associated with the underlying metacyclic group. Such codes in the same group ring are isomorphic as vector spaces but may vary greatly in weight distributions and so are nonequivalent. If the associated cyclic code is irreducible, examining the structure of its isomorphic finite field yields all nonequivalent codes with the desired structure. Several such codes have been found to have minimum distances equalling those of the best known linear codes of the same length and dimension.

Using a genetic algorithm to find good linear error-correcting codes

A genetic algorithm is used to search for linear binary codes with optimal minimum distance for a fixed length n and dimension k. Several modifications to the algorithm are compared to find an algorithm best suited to this application. The code is parallelized and mn on a multi-processor and speedup determined.

The use of parallelization in the generation of binary linear codes

Digital data can be distorted in transmission or damaged as a result of trauma to the storage medium. Errorcorrecting codes provide a method of detecting and correcting such errors. Data is encoded by affting extra bits that result from relationships among the bits of the original data. After storage or transmission, the mathematical process is reversed and errors detected and corrected to produce the original information. “Good” codes correct errors while keeping to a minimum the number of extra, redundant bits that are added so that the transmission rate can be kept reasonably high.

Integrating recent research results into undergraduate curricula (panel): initial steps

On July 7-11, 60 computer scientists came together at The Evergreen State College in Olympia, Washington to consider how the undergraduate curricula might be improved in light of recent research in computer science. At this NSF-funded workshop, researchers presented work in four areas where current research might be particularly relevant, and undergraduate faculty (with experience in software engineering, functional programming, artificial intelligence, discrete mathematics or theoretical computer science) explored the current state of undergraduate computer science curricula and ways in which they might be better informed by recent research.Each participant attended sessions in one of the four interest areas--Software Engineering Capstone Courses, Functional Programming, Neural Networks and Their Applications, and Computational Geometry--and faculty developed curricular materials that they could use in their teaching the following year. Those materials are being placed on the WWW, and faculty are refining them as they use them in their courses. A second workshop is planned for summer, 1998.The workshop was sponsored by The Evergreen State College, the Oregon Graduate Institute, the Washington Center for the Improvement of Undergraduate Education, and by the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS).All of the panelists participated in the workshop and each panel member will share his or her experiences in incorporating the recent research results studied at the workshop into their undergraduate curriculum. In addition, the panelists will discuss with the audience their own plans for integrating research results into their own undergraduate programs.