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Quantum error-correcting codes from algebraic curves
| Content Provider | Semantic Scholar |
|---|---|
| Author | Kim, Jon-Lark Matthews, Gretchen L. |
| Copyright Year | 2008 |
| Abstract | This chapter discusses quantum error-correcting codes constructed from algebraic curves. We give an introduction to quantum coding theory including bounds on quantum codes. We describe stabilizer codes which are the quantum analog of classical linear codes and discuss the binary and q-ary CSS construction. Then we focus on quantum codes from algebraic curves including the projective line, Hermitian curves, and hyperelliptic curves. In addition, we describe the asymptotic behaviors of quantum codes from the Garcia-Stichtenoth tower attaining the Drinfeld-Vlăduţ bound. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.math.clemson.edu/~gmatthe/chapter_13_final.pdf |
| Alternate Webpage(s) | http://www.math.louisville.edu/~jlkim/chapter_13_final.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Analog Behavior Bitwise operation Cascading Style Sheets Coding theory Coffin-Siris syndrome Error detection and correction Forward error correction Linear algebra Quantum error correction Quantum programming Stabilizer code |
| Content Type | Text |
| Resource Type | Article |