Algorithmic Approach for Error-Correcting Capability and Decoding of Linear Codes Arising from Algebraic Geometry

2018 ◽  
pp. 509-517
Author(s):  
Arunkumar Patil ◽  
Nitin Darkunde
Keyword(s):  
Algebraic Geometry ◽  
Linear Codes ◽  
Algorithmic Approach

scholarly journals Steiner systems and configurations of points

2020 ◽  
Author(s):  
Edoardo Ballico ◽  
Giuseppe Favacchio ◽  
Elena Guardo ◽  
Lorenzo Milazzo
Keyword(s):  
Algebraic Geometry ◽  
Commutative Algebra ◽  
Design Theory ◽  
Hilbert Function ◽  
Linear Codes ◽  
Betti Numbers ◽  
Steiner System ◽  
Steiner Systems ◽  
Waldschmidt Constant ◽  
The Ideal

Abstract The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System S(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study symbolic and regular powers associated to the ideal defining a Complement of a Steiner configuration of points, finding its Waldschmidt constant, regularity, bounds on its resurgence and asymptotic resurgence. We also compute the parameters of linear codes associated to any Steiner configuration of points and its Complement.

Granular Gain of Low-Dimensional Lattices from Binary Linear Codes

2012 ◽  
Vol E95.A (12) ◽  
pp. 2168-2170
Author(s):  
Misako KOTANI ◽  
Shingo KAWAMOTO ◽  
Motohiko ISAKA
Keyword(s):  
Linear Codes ◽  
Binary Linear Codes ◽  
Low Dimensional

Algorithmic Approach to Analysis of Queuing System with Finite Queues and Jump-like Priorities

2012 ◽  
Vol 44 (12) ◽  
pp. 43-54 ◽  
Author(s):  
Agasi Zarbali ogly Melikov ◽  
Leonid A. Ponomarenko ◽  
Che Soong Kim
Keyword(s):  
Queuing System ◽  
Algorithmic Approach ◽  
Finite Queues
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