scholarly journals Generalized AG Codes as Evaluation Codes

2013 ◽  
pp. 74-82
Author(s):  
Marco Calderini ◽  
Massimiliano Sala
Keyword(s):  
Evaluation Codes ◽  
Ag Codes

scholarly journals List decoding algorithm based on voting in Gröbner bases for general one-point AG codes

2017 ◽  
Vol 79 ◽  
pp. 384-410
Author(s):  
Ryutaroh Matsumoto ◽  
Diego Ruano ◽  
Olav Geil
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
List Decoding ◽  
Decoding Algorithm ◽  
Ag Codes

AG codes from vector bundles

2009 ◽  
Vol 57 (1) ◽  
pp. 107-115 ◽  
Author(s):  
Tohru Nakashima
Keyword(s):  
Vector Bundles ◽  
Ag Codes

scholarly journals Improved Decoding of Interleaved AG Codes

2005 ◽  
pp. 37-46 ◽  
Author(s):  
Andrew Brown ◽  
Lorenz Minder ◽  
Amin Shokrollahi
Keyword(s):  
Ag Codes

Analogues of AG-Codes

1991 ◽  
pp. 567-593
Author(s):  
M. A. Tsfasman ◽  
S. G. Vlăduţ
Keyword(s):  
Ag Codes

Efficient Forney functions for decoding AG codes

1999 ◽  
Vol 45 (1) ◽  
pp. 260-265 ◽  
Author(s):  
D.A. Leonard
Keyword(s):  
Ag Codes

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 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.

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