Abstract
In this paper, we present quantum codes via algebraic geometry codes on norm-trace curves. We provide a lower bound of minimum Hamming distance for q-ary quantum code, where q = 2e (e ≥ 3). In order to get this, we determine Feng-Rao function values for the elements of Weierstrass semigroups on norm-trace curves. We present the order-bound on the minimum Hamming distance of one-point dual codes. Furthermore, we give a certain increasing sequence of one-point codes on norm-trace curves. We construct quantum codes from the sequence of one-point codes via the CSS construction. These give a better lower bound on the minimum Hamming distance of q-ary quantum code than some previous results.
Original language | English |
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Pages (from-to) | 1179-1188 |
Number of pages | 10 |
Journal | Cryptography and Communications |
Volume | 14 |
Issue number | 5 |
DOIs | |
State | Published - Sep 2022 |
Keywords
- Algebraic geometry code
- Dual code
- Norm-trace curve
- One-point code
- Quantum code