Fundamentals of Error-correcting Codes - Notes

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...

Lecture Notes

In this lecture notes, the forward error correction (FEC) codes relevant to the establishment of reliable communication are presented. The accompanying flowchart provides an overview and indicates the linkage between different sections. Sections 2 through 10 present the principles of error correction and provide background material on most of the FEC codes used. General binary error correcting ...

Coding Theory Lecture Notes

These are the notes for the 2011 Summer Tutorial on Coding Theory. I have not gone through and given citations or references for all of the results given here, but the presentation relies heavily on two sources, van Lint’s Introduction to Coding Theory and the book of Huffman and Pless Fundamentals of Error-Correcting Codes. I also used course notes written by Sebastian Pancratz from a Part II ...

Lecture Notes for Mathematics 601 Error Correcting Codes and Algebraic Curves

An approach to fault detection and correction in design of systems using of Turbo ‎codes‎

We present an approach to design of fault tolerant computing systems. In this paper, a technique is employed that enable the combination of several codes, in order to obtain flexibility in the design of error correcting codes. Code combining techniques are very effective, which one of these codes are turbo codes. The Algorithm-based fault tolerance techniques that to detect errors rely on the c...