Nonbinary quantum error-correcting codes from algebraic curves

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• 作者：Jon-Lark Kim ; Judy Walker
• 关键词：Algebraic geometric codes ; Nonbinary quantum codes
• 刊名：Discrete Mathematics
• 出版年：2008
• 出版时间：28 July 2008
• 年：2008
• 卷：308
• 期：14
• 页码：3115-3124
• 全文大小：199 K

文摘

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.