I‑AIMS Institute for Artificial Intelligence
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Quantum Codes from Algebraic Curves with Automorphisms

Tanush Shaska

I-AIMS paper 2007-5 ยท Published in Condensed Matter Phys. 11 (2008), no. 2(54), 383โ€“396 ยท 2008

Let ๐’ณ be an algebraic curve of genus g โ‰ฅ 2 defined over a field ๐”ฝ_q of characteristic p > 0. From ๐’ณ, 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 ๐’ณ and the codes C and Q.

MSC classes: Primary 94B27; Secondary 81P70, 14H37

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