I‑AIMS Institute for Artificial Intelligence
and Mathematical Sciences
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Quantum codes from superelliptic curves

Artur Elezi, Tanush Shaska

I-AIMS paper 2011-1 · Published in Albanian J. Math. 5 (2011), 175–191 · 2011

Let 𝒳 be an algebraic curve of genus g ≥ 2 defined over a field 𝔽_q 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.

MSC classes: Primary 94B27; Secondary 81P70, 94B15

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