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Nonbinary Quantum Error-Correcting Codes From Algebraic Curves, Jon-Lark Kim, Judy L. Walker
Nonbinary Quantum Error-Correcting Codes From Algebraic Curves, Jon-Lark Kim, Judy L. Walker
Department of Mathematics: Faculty Publications
We give a generalized CSS construction for nonbinary quantum error-correcting codes. Using this we construct nonbinary quantum stabilizer codes from algebraic curves. We also give asymptotically good nonbinary quantum codes from a Garcia- Stichtenoth tower of function fields which are constructible in polynomial time.
Binary quantum error-correcting codes have been constructed in several ways. One interesting construction uses algebraic-geometry codes [2], [6], [7], [12], with the main idea being to apply the binary CSS construction [4], [5], [16] to the asymptotically good algebraic-geometry codes arising from the Garcia-Stichtenoth [11] tower of function fields over Fq2 (where q is a …