Evaluation codes and weierstrass semigroups

2015 ◽  
Vol 49 (1) ◽  
pp. 22-22
Author(s):  
Emma Previato
Keyword(s):  
Evaluation Codes ◽  
Weierstrass Semigroups

scholarly journals Automorphisms of curves and Weierstrass semigroups for Harbater–Katz–Gabber covers

2019 ◽  
Vol 371 (9) ◽  
pp. 6377-6402 ◽  
Author(s):  
Sotiris Karanikolopoulos ◽  
Aristides Kontogeorgis
Keyword(s):  
Weierstrass Semigroups

scholarly journals Ideals of Numerical Semigroups and Error-Correcting Codes

Symmetry ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 1406
Author(s):  
Bras-Amorós
Keyword(s):  
Secret Sharing ◽  
Error Correcting Codes ◽  
Numerical Semigroups ◽  
Secret Sharing Schemes ◽  
List Decoding ◽  
Generalized Hamming Weights ◽  
Resilient Functions ◽  
Weierstrass Semigroups ◽  
Hamming Weights ◽  
Dual Sequences

Several results relating additive ideals of numerical semigroups and algebraic-geometrycodes are presented. In particular, we deal with the set of non-redundant parity-checks, the codelength, the generalized Hamming weights, and the isometry-dual sequences of algebraic-geometrycodes from the perspective of the related Weierstrass semigroups. These results are related tocryptographic problems such as the wire-tap channel, t-resilient functions, list-decoding, networkcoding, and ramp secret sharing schemes.

scholarly journals Bounding the Number of Common Zeros of Multivariate Polynomials and Their Consecutive Derivatives

2018 ◽  
Vol 28 (2) ◽  
pp. 253-279
Author(s):  
O. GEIL ◽  
U. MARTÍNEZ-PEÑAS
Keyword(s):  
Upper Bound ◽  
Existence And Uniqueness ◽  
Combinatorial Nullstellensatz ◽  
Finite Collection ◽  
Multivariate Polynomials ◽  
Grobner Basis ◽  
Evaluation Codes ◽  
Number Of Zeros ◽  
Interpolating Polynomials ◽  
Common Zeros

We upper-bound the number of common zeros over a finite grid of multivariate polynomials and an arbitrary finite collection of their consecutive Hasse derivatives (in a coordinate-wise sense). To that end, we make use of the tool from Gröbner basis theory known as footprint. Then we establish and prove extensions in this context of a family of well-known results in algebra and combinatorics. These include Alon's combinatorial Nullstellensatz [1], existence and uniqueness of Hermite interpolating polynomials over a grid, estimations of the parameters of evaluation codes with consecutive derivatives [20], and bounds on the number of zeros of a polynomial by DeMillo and Lipton [8], Schwartz [25], Zippel [26, 27] and Alon and Füredi [2]. As an alternative, we also extend the Schwartz-Zippel bound to weighted multiplicities and discuss its connection to our extension of the footprint bound.

scholarly journals Weierstrass semigroups on the Giulietti–Korchmáros curve

2018 ◽  
Vol 52 ◽  
pp. 10-29 ◽  
Author(s):  
Peter Beelen ◽  
Maria Montanucci
Keyword(s):  
Weierstrass Semigroups

scholarly journals Description of a Computer Program to Assess Cancer Antigen 15.3, Carcinoembryonic Antigen, and Tissue Polypeptide Antigen Information during Monitoring of Metastatic Breast Cancer

2000 ◽  
Vol 46 (8) ◽  
pp. 1106-1113 ◽  
Author(s):  
György Sölétormos ◽  
Vibeke Schiøler
Keyword(s):  
Breast Cancer ◽  
Computer Program ◽  
Cancer Patients ◽  
Metastatic Breast ◽  
Biological Variation ◽  
Clinical Activity ◽  
Assessment Procedure ◽  
Breast Cancer Patients ◽  
Evaluation Codes ◽  
Treatment Type

Abstract It is time-consuming to process and compare the clinical and marker information registered during monitoring of breast cancer patients. To facilitate the assessment, we developed a computer program for interpreting consecutive measurements. The intraindividual biological variation, the analytical precision profile, the cutoff limit, and the detection limit for each marker are entered and stored in the program. The assessment procedure for marker signals considers the analytical and biological variation of the applied markers. The software package contains a database that can store the interpretation of the measurements as evaluation codes together with patient demographics, information about treatment type, dates for treatment periods, control periods, and evaluation codes for clinical activity of disease. The consecutive concentrations for a patient are imported temporarily into the program from outside sources and presented graphically. Marker concentrations to be compared are selected with the computer mouse and the significance of the difference is calculated by the program. The program has an option for calculating the lead time of marker signals vs clinical information. The program facilitates the monitoring of individual breast cancer patients with tumor marker measurements. It may also be implemented in trials investigating the utility of potential new markers in breast cancer as well as in other malignancies.

scholarly journals Generalized Weierstrass semigroups and their Poincaré series

2019 ◽  
Vol 58 ◽  
pp. 46-69
Author(s):  
J.J. Moyano-Fernández ◽  
W. Tenório ◽  
F. Torres
Keyword(s):  
Poincaré Series ◽  
Poincare Series ◽  
Weierstrass Semigroups
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