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Nonbinary quantum error-correcting codes from algebraic curves |
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| Authors: | Jon-Lark Kim Judy Walker |
| Institution: | aDepartment of Mathematics, University of Louisville, Louisville, KY 40292, USA bDepartment of Mathematics, University of Nebraska – Lincoln, Lincoln, NE 68588, USA |
| Abstract: | We give a new exposition and proof of a generalized CSS construction for nonbinary quantum error-correcting codes. Using this we construct nonbinary quantum stabilizer codes with various lengths, dimensions, and minimum distances 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. |
| Keywords: | Algebraic geometric codes Nonbinary quantum codes |
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