Quantum codes from one-point codes on norm-trace curves

초록

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 = 2(e) (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.

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