Graph theoretic 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...

Ideal Error-Correcting Codes: Unifying Algebraic and Number-Theoretic Algorithms

Over the past five years a number of algorithms decoding some well-studied error-correcting codes far beyond their “error-correcting radii” have been developed. These algorithms, usually termed as listdecoding algorithms, originated with a list-decoder for Reed-Solomon codes [36, 17], and were soon extended to decoders for Algebraic Geometry codes [33, 17] and as also some number-theoretic code...

On multiple insertion/Deletion correcting codes

We investigate binary, number-theoretic, bit insertion/deletion correcting codes as pioneered by Levenshtein. The weight spectra and Hamming distance properties of single insertion/deletion error-correcting codes are analyzed. These relationships are then extended to investigate codes that can correct multiple random insertions and deletions. From these relationships, new bounds are derived and...

A Graph-Theoretic Approach to Bounds for Error-Correcting Codes CIMPA-UNESCO-PHILIPPINES Summer School on Semidefinite Programming in Algebraic Combinatorics

In these notes, we address bounds for error-correcting codes. Our approach is from the viewpoint of algebraic graph theory. We therefore begin with a review of the algebraic structure of the Hamming graph, focusing on the binary case. We then derive Delsarte’s linear programming bound and explore some applications of it. In the second part of the notes, we introduce Terwilliger’s subconstituent...

Ideal Error-correcting codes: Unifying Algebraic and Number-theoretic Algorithms