Lecture 1 : Error - Correcting Codes ; Vector Spaces Week 1 UCSB 2015 1 Error - Correcting Codes

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...

Intro to Quantum Computation Semester B 2001 Scribe for Lecture on Quantum Error Correcting Codes Quantum Error Correcting Codes Introduction to Quantum Computation

A note on an upper bound of traceability codes

Blackburn, Etzion and Ng showed in a paper in 2010 that there exist 2-traceability codes of length l of size cqdl/4e, where the constant c depends only on l. The question remains as to what the best possible c may be. A well-known construction using error-correcting codes with high minimum distance gives 2-traceability codes of size cqdl/4e with c ≥ 1. However, in the same paper, an example of ...

Error Correcting Codes And Their Implementation

We consider dictionaries of size n over the finite universe u = (0, l)w and introduce a new technique for their implementation: error correcting codes. protected with an error-correcting code (ECC) is presented in this compared with the most recent implementation. treated within industries for their products. ―VLSI Implementation of Decoder Error Correcting in Satellite. Concatenation Code in F...

On the Triple-Error-Correcting Cyclic Codes

We consider a class of 3-error-correcting cyclic codes of length 2−1 over the two-element field F2. The generator polynomial of a code of this class has zeroes α, α i +1 and α j , where α is a primitive element of the field F2m . In short, {1, 2+1, 2 +1} refers to the zero set of these codes. Kasami in 1971 and Bracken and Helleseth in 2009, showed that cyclic codes with zeroes {1, 2 + 1, 2 + 1...