Decay of Correlations for Sparse Graph Error Correcting Codes

Epileptic seizure detection based on The Limited Penetrable visibility graph algorithm and graph properties

Introduction: Epileptic seizure detection is a key step for both researchers and epilepsy specialists for epilepsy assessment due to the non-stationariness and chaos in the electroencephalogram (EEG) signals. Current research is directed toward the development of an efficient method for epilepsy or seizure detection based the limited penetrable visibility graph (LPVG) algorith...

Good Quantum Error-Correcting Codes based on Sparse Graphs

Graph based linear error correcting codes

In this article we present a construction of error correcting codes, that have representation as very sparse matrices and belong to the class of Low Density Parity Check Codes. LDPC codes are in the classical Hamming metric. They are very close to well known Shannon bound. The ability to use graphs for code construction was first discussed by Tanner in 1981 and has been used in a number of very...

Gallager Codes – Recent Results

In 1948, Claude Shannon posed and solved one of the fundamental problems of information theory. The question was whether it is possible to communicate reliably over noisy channels, and, if so, at what rate. He defined a theoretical limit, now known as the Shannon limit, up to which communication is possible, and beyond which communication is not possible. Since 1948, coding theorists have attem...

One-point Goppa Codes on Some Genus 3 Curves with Applications in Quantum Error-Correcting Codes

We investigate one-point algebraic geometric codes CL(D, G) associated to maximal curves recently characterized by Tafazolian and Torres given by the affine equation yl = f(x), where f(x) is a separable polynomial of degree r relatively prime to l. We mainly focus on the curve y4 = x3 +x and Picard curves given by the equations y3 = x4-x and y3 = x4 -1. As a result, we obtain exact value of min...