Quantum Goppa Codes over Hyperelliptic Curves

Details Quantum Goppa Codes over Hyperelliptic Curves Quantum Goppa Codes over Hyperelliptic Curves

2005-01-14

arxiv.org/abs/quant-ph/0501074v1

Physics

Quantum Physics

93 pages

Scientific paper

This Diplom thesis provides an explicit construction of a quantum Goppa code for any hyperelliptic curve over a non-binary field. Hyperelliptic curves have conjugate pairs of rational places. We use these pairs to construct self-orthogonal classical Goppa codes with respect to a weighted inner product. These codes are also self-orthogonal with respect to a symplectic inner product and therefore define quantum stabilizer codes. A final transformation leads to a quantum Goppa code with respect to the standard symplectic inner product. Some examples illustrate the described construction. Furthermore we present a projection of a higher dimensional code onto the base field and a special case when the projected code is again weighted self-orthogonal and symmetric.

Affiliated with

Also associated with

No associations

Rating

Quantum Goppa Codes over Hyperelliptic Curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Goppa Codes over Hyperelliptic Curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Goppa Codes over Hyperelliptic Curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-88185