The quantum MDS conjecture

Prove that stabilizer quantum MDS codes on qudits of dimension q have length at most q²+1, apart from one even-q family, or find a longer one.

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1	{
2	"domain": "physics-astronomy",
3	"topics": [
4	"quantum-information",
5	"coding-theory"
6	],
7	"type": "proof",
8	"also": [
9	"construction"
10	],
11	"cover": {
12	"motif": "spheres"
13	},
14	"source": {
15	"key": "qiqcop",
16	"name": "QIQCOP Zoo",
17	"url": "https://qiqc-op.com/problem/op_2a6fc2b70a85f846/",
18	"id": "op_2a6fc2b70a85f846",
19	"curator": "Bikun Li, Qicheng Tang, Changhao Li, Chengkai Zhu, Minbo Gao, Zhong-Xia Shang, Bin Cheng and Naixu Guo",
20	"poser": "Avanti Ketkar, Andreas Klappenecker, Santosh Kumar and Pradeep Kiran Sarvepalli",
21	"status": "unsolved",
22	"as_of": "2026-10-20",
23	"catalog": "0521c19bbd38"
24	},
25	"review": true,
26	"approval": "first-time"
27	}