12 research outputs found
A linear construction for certain Kerdock and Preparata codes
The Nordstrom-Robinson, Kerdock, and (slightly modified) Pre\- parata codes
are shown to be linear over \ZZ_4, the integers . The Kerdock and
Preparata codes are duals over \ZZ_4, and the Nordstrom-Robinson code is
self-dual. All these codes are just extended cyclic codes over \ZZ_4. This
provides a simple definition for these codes and explains why their Hamming
weight distributions are dual to each other. First- and second-order
Reed-Muller codes are also linear codes over \ZZ_4, but Hamming codes in
general are not, nor is the Golay code.Comment: 5 page
Quaternary codes and their binary images
Recently, simplicial complexes are used in constructions of several infinite
families of minimal and optimal linear codes by Hyun {\em et al.} Building upon
their research, in this paper more linear codes over the ring
are constructed by simplicial complexes. Specifically, the Lee weight
distributions of the resulting quaternary codes are determined and two infinite
families of four-Lee-weight quaternary codes are obtained. Compared to the
databases of codes by Aydin {\em et al.}, at least nine new
quaternary codes are found. Thanks to the special structure of the defining
sets, we have the ability to determine whether the Gray images of certain
obtained quaternary codes are linear or not. This allows us to obtain two
infinite families of binary nonlinear codes and one infinite family of binary
minimal linear codes. Furthermore, utilizing these minimal binary codes, some
secret sharing schemes as a byproduct also are established.Comment: 21 page
Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories
Several physical effects that limit the reliability and performance of multilevel flash memories induce errors that have low magnitudes and are dominantly asymmetric. This paper studies block codes for asymmetric limited-magnitude errors over q-ary channels. We propose code constructions and bounds for such channels when the number of errors is bounded by t and the error magnitudes are bounded by â. The constructions utilize known codes for symmetric errors, over small alphabets, to protect large-alphabet symbols from asymmetric limited-magnitude errors. The encoding and decoding of these codes are performed over the small alphabet whose size depends only on the maximum error magnitude and is independent of the alphabet size of the outer code. Moreover, the size of the codes is shown to exceed the sizes of known codes (for related error models), and asymptotic rate-optimality results are proved. Extensions of the construction are proposed to accommodate variations on the error model and to include systematic codes as a benefit to practical implementation
Application of Geographic Information Systems
The importance of Geographic Information Systems (GIS) can hardly be overemphasized in todayâs academic and professional arena. More professionals and academics have been using GIS than ever â urban & regional planners, civil engineers, geographers, spatial economists, sociologists, environmental scientists, criminal justice professionals, political scientists, and alike. As such, it is extremely important to understand the theories and applications of GIS in our teaching, professional work, and research. âThe Application of Geographic Information Systemsâ presents research findings that explain GISâs applications in different subfields of social sciences. With several case studies conducted in different parts of the world, the book blends together the theories of GIS and their practical implementations in different conditions. It deals with GISâs application in the broad spectrum of geospatial analysis and modeling, water resources analysis, land use analysis, infrastructure network analysis like transportation and water distribution network, and such. The book is expected to be a useful source of knowledge to the users of GIS who envision its applications in their teaching and research. This easy-to-understand book is surely not the end in itself but a little contribution to toward our understanding of the rich and wonderful subject of GIS
Esprit '91. Proceedings of the annual Esprit conference. Brussels, 25-29 November 1991. EUR 13853 EN
Phylogenetic structural modeling of molecular evolution
ThÚse numérisée par la Direction des bibliothÚques de l'Université de Montréal