Quantum codes from algebraic curves with automorphisms
Let X be an algebraic curve of genus g ≥ 2 defined over a field Fq of characteristic p > 0. From X, under certain conditions, we can construct an algebraic geometry code C. If the code C is self-orthogonal under the symplectic product then we can construct a quantum code Q, called a QAG-code. In...
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| Published in: | Condensed Matter Physics |
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| Date: | 2008 |
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| Format: | Article |
| Language: | English |
| Published: |
Інститут фізики конденсованих систем НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/119289 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Quantum codes from algebraic curves with automorphisms / T. Shaska // Condensed Matter Physics. — 2008. — Т. 11, № 2(54). — С. 383-396. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Let X be an algebraic curve of genus g ≥ 2 defined over a field Fq of characteristic p > 0. From X, under certain conditions, we can construct an algebraic geometry code C. If the code C is self-orthogonal under the symplectic product then we can construct a quantum code Q, called a QAG-code. In this paper we study the construction of such codes from curves with automorphisms and the relation between the automorphism group of the curve X and the codes C and Q.
Нехай – алгебраїчна крива типу g ≥ 2, що визначена над полем Fq характеристики p. При деяких умовах на ми можемо будувати алгебраїчно-геометричний код C. Якщо код C є самоортогональним вiдповiдно до симплектичного добутку, то будується квантовий код Q, який будемо називати QAC кодом. В статтi вивчаються конструкцiї таких кодiв за кривими з автоморфiзнами i зв’язки мiж групами автоморфiзмiв кривої та кодiв C та Q.
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| ISSN: | 1607-324X |