List Decoding Algorithm based on Voting in Groebner Bases for General One-Point AG Codes

We generalize the unique decoding algorithm for one-point AG codes over the Miura-Kamiya Cab curves proposed by Lee, Bras-Amor\'os and O'Sullivan (2012) to general one-point AG codes, without any assumption. We also extend their unique decoding algorithm to list decoding, modify it so that it can be used with the Feng-Rao improved code construction, prove equality between its error correcting capability and half the minimum distance lower bound by Andersen and Geil (2008) that has not been done in the original proposal except for one-point Hermitian codes, remove the unnecessary computational steps so that it can run faster, and analyze its computational complexity in terms of multiplications and divisions in the finite field. As a unique decoding algorithm, the proposed one is empirically and theoretically as fast as the BMS algorithm for one-point Hermitian codes. As a list decoding algorithm, extensive experiments suggest that it can be much faster for many moderate size/usual inputs than the algorithm by Beelen and Brander (2010). It should be noted that as a list decoding algorithm the proposed method seems to have exponential worst-case computational complexity while the previous proposals (Beelen and Brander, 2010; Guruswami and Sudan, 1999) have polynomial ones, and that the proposed method is expected to be slower than the previous proposals for very large/special inputs.Comment: Accepted for publication in J. Symbolic Computation. LaTeX2e article.cls, 42 pages, 4 tables, no figures. Ver. 6 added an illustrative example of the algorithm executio

Pharmacokinetic Properties of Liraglutide as Adjunct to Insulin in Subjects with Type 1 Diabetes Mellitus.

BACKGROUND: The pharmacokinetic properties of liraglutide, a glucagon-like peptide-1 receptor agonist approved for the treatment of type 2 diabetes mellitus (T2D), have been established in healthy individuals and subjects with T2D. Liraglutide has been under investigation as adjunct treatment to insulin in type 1 diabetes mellitus (T1D). This single-center, double-blind, placebo-controlled, crossover, clinical pharmacology trial is the first to analyze the pharmacokinetic properties of liraglutide as add-on to insulin in T1D. METHODS: Subjects (18-64 years; body mass index 20.0-28.0 kg/m(2); glycated hemoglobin ≤9.5 %) were randomized 1:1:1 to 0.6, 1.2, or 1.8 mg liraglutide/placebo. Each group underwent two 4-week treatment periods (liraglutide then placebo or placebo then liraglutide) separated by a 2- to 3-week washout. Both trial drugs were administered subcutaneously, once daily, as adjunct to insulin. A stepwise hypoglycemic clamp was performed at the end of each treatment period (data reported previously). Pharmacokinetic endpoints were derived from liraglutide concentration-time curves after the final dose and exposure was compared with data from previous trials in healthy volunteers and subjects with T2D. RESULTS: The pharmacokinetic properties of liraglutide in T1D were comparable with those observed in healthy volunteers and subjects with T2D. Area under the steady-state concentration-time curve (AUC) and maximum plasma concentration data were consistent with dose proportionality of liraglutide. Comparison of dose-normalized liraglutide AUC suggested that exposure in T1D, when administered with insulin, is comparable with that observed in T2D. CONCLUSIONS: Liraglutide, administered as adjunct to insulin in subjects with T1D, shows comparable pharmacokinetics to those in subjects with T2D. ClinicalTrials.gov Identifier: NCT01536665

Double Series Representation of Bounded Signals

... for bounded signals f(t) are studied, as are conditions on the unit function v(r), such that the coefficients a,, k reveal the energy content of f(t) in the time interval n-(l/2) < t I n +(1/2) and frequency interval 2m(k-(l/2)) I w I 2n(k +(1/2)). These conditions turn out to he 1) orthogonal&y, i.e., and 2) integrability, v(r) EL!(R) V(w) E L’(R). if n=k=O otherwise Based on these conditions a number of properties of the expansion are derived, including smmnability of the double series and energy and power estimations. A unit function u(t) is constructed which is optimal, within a restricted class, with respect to the duration of V(w), and also a unit function which is optimal with respect to the duration of u(t). Finally, some examples of the expansion are presented

Performance analysis of a decoding algorithm for algebraic-geometry codes

The fast decoding algorithm for one point algebraic geometry codes of Sakata, Elbrnd Jensen and Hholdt corrects all error patterns of weight less than half the Feng-Rao minimum distance. In this paper we analyse the performance of the algorithm for heavier error patterns. It turns out that in the typical case where the error points are "independent"one can prove that the algorithm always fails, that is gives a wrong or no answer, except for high rates where it does much better than expected. This explains the simulation results presented by O'Sullivan at the 1997 ISIT. We also show that for dependent errors the algorithm almost always corrects these. Keywords Decoding, Algebraic Geometry Codes, Performance. I. Introduction. O NE of the main problems in decoding is to analyse the performance of a decoding algorithm when the error pattern has weight greater than half the minimum distance of the code. Recently M. O'Sullivan [1] presented simulation results for some Hermitian Codes and..