In this paper, we study cyclic codes of length n= 2/sup e/ over the ring R/sub 4/= /spl Zopf//sub 4/[x]/(x/sup n/-1). In particular, we derive a mass formula of these codes for a given length n. We also give an example in which we study codes of length 8.

In this correspondence, we study cyclic codes of length n=2/sup e/ over the ring R/sub 4/=/spl Zopf//sub 4/[x]/(x/sup n/-1). In particular, we derive a closed-form expression for the number of these codes for a given length n. We also study the rank of these codes and derive an expression for that. Furthermore, we give an example in which we study all cyclic codes of length 8. We also study all self-dual codes of length 8 and 16 and classify them according to their type.

Results are presented on the generators of ideals in the ring /spl Zopf//sub 4/[x]/(x/sup n/-1). In particular, each ideal (cyclic code) has a unique distinguished set of generators that characterizes any cyclic code. Some results about dual codes are also included.

We present a scalable, high-performance solution to multidimensional recurrences that arise in adaptive statistical designs. Adaptive designs are an important class of learning algorithms for a stochastic environment, and we focus on the problem of optimally assigning patients to treatments in clinical trials. While adaptive designs have significant ethical and cost advantages, they are rarely utilized because of the complexity of optimizing and analyzing them. Computational challenges include massive memory requirements, few calculations per memory access, and multiply-nested loops with dynamic indices. We analyze the effects of various parallelization options, and while standard approaches do not work well, with effort an efficient, highly scalable program can be developed. This allows us to solve problems thousands of times more complex than those solved previously, which helps make adaptive designs practical. Further, our work applies to many other problems involving neighbor recurrences, such as generalized string matching.

article Free Access Share on 𝒮-Semigroups of Automata Authors: A. C. Fleck Department of Computer Science, The University of Iowa, Iowa City, Iowa Department of Computer Science, The University of Iowa, Iowa City, IowaView Profile , S. T. Hedetniemi Department of Computer Science, The University of Iowa, Iowa City, Iowa Department of Computer Science, The University of Iowa, Iowa City, IowaView Profile , R. H. Oehmke Department of Mathematics, The University of Iowa, Iowa City, Iowa Department of Mathematics, The University of Iowa, Iowa City, IowaView Profile Authors Info & Claims Journal of the ACMVolume 19Issue 1Jan. 1972 pp 3–10https://doi.org/10.1145/321679.321681Published:01 January 1972Publication History 6citation314DownloadsMetricsTotal Citations6Total Downloads314Last 12 Months9Last 6 weeks0 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

In this paper, relationships are developed between the structure of an automaton A and the structure of its input semigroup S. For a particular class of automata called "cyclic" automata it is shown that each member of this class can be realized as an intrinsic structure on the semigroup S.With such relationships existing it seems possible that greater use can be made of the existing literature on the structures of semigroups in the algebraic theory of automata.In Section 1 preliminary definitions and results are stated, most of which are essentially contained in Rabin and Scott [3] and Clifford [1; Sections 1.4 and 1.5].They are included here for clarity of presentation.In Section 2 some of the relationships between the two systems are established.In Section 3 an ~pplication is made to the isomorphism group of A.