Good Stabilizer Codes from Quasi-Cyclic Codes over $\mathbb{F}_4$ and $\mathbb{F}_9$

Buket \"Ozkaya; Martianus Frederic Ezerman; Patrick Sol\'e; San Ling

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Good Stabilizer Codes from Quasi-Cyclic Codes over mathbb{F}₄ and mathbb{F}₉

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arxiv 1906.04964 v1 pith:UWL4SFBB submitted 2019-06-12 cs.IT math.IT

Good Stabilizer Codes from Quasi-Cyclic Codes over mathbb{F}₄ and mathbb{F}₉

Martianus Frederic Ezerman , San Ling , Buket \"Ozkaya , Patrick Sol\'e This is my paper

classification cs.IT math.IT

keywords codesmathbbquantumconstructiongoodobtainoccasionsquasi-cyclic

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We apply quantum Construction X on quasi-cyclic codes with large Hermitian hulls over $\mathbb{F}_4$ and $\mathbb{F}_9$ to derive good qubit and qutrit stabilizer codes, respectively. In several occasions we obtain quantum codes with stricly improved parameters than the current record. In numerous other occasions we obtain quantum codes with best-known performance. For the qutrit ones we supply a systematic construction to fill some gaps in the literature.

Good Stabilizer Codes from Quasi-Cyclic Codes over mathbb{F}₄ and mathbb{F}₉

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