Bounds on the minimum distance of additive quantum codes
Bounds on [[77,0]]2
| lower bound: | 19 |
| upper bound: | 27 |
Construction
Construction type: SeneviratneCuffKoletsosSeekampThnanopavarn
Construction of a [[77,0,19]] quantum code:
[1]: [[77, 0, 19]] self-dual quantum code over GF(2^2)
cyclic code of length 77 with generating polynomial w^2*x^76 + x^75 + w*x^74 + x^73 + w^2*x^71 + w*x^69 + w^2*x^68 + w*x^66 + w^2*x^64 + w*x^63 + w^2*x^61 + w*x^60 + w^2*x^59 + w*x^57 + w*x^54 + w*x^53 + w^2*x^52 + x^51 + w*x^50 + x^48 + x^47 + x^46 + w^2*x^45 + w*x^41 + w*x^40 + w*x^39 + w*x^38 + w*x^36 + w*x^33 + w*x^32 + 1
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1|0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1]
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last modified: 2023-09-12
Notes
- All codes establishing the lower bounds where constructed using MAGMA.
- Most upper bounds on qubit codes for n≤100 are based on a MAGMA program by Eric Rains.
- For n>100, the upper bounds on qubit codes are weak (and not necessarily monotone in k).
- Some additional information can be found in the book by Nebe, Rains, and Sloane.
- My apologies to all authors that have contributed codes to this table for not giving specific credits.
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Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024