Bounds on the minimum distance of additive quantum codes
Bounds on [[90,0]]2
| lower bound: | 22 |
| upper bound: | 32 |
Construction
Construction type: SeneviratneCuffKoletsosSeekampThnanopavarn
Construction of a [[90,0,22]] quantum code:
[1]: [[90, 0, 22]] self-dual quantum code over GF(2^2)
cyclic code of length 90 with generating polynomial w^2*x^89 + x^87 + w^2*x^86 + w*x^85 + w^2*x^84 + w*x^83 + w*x^82 + x^81 + w^2*x^79 + w*x^78 + w^2*x^77 + w*x^76 + w^2*x^74 + w^2*x^73 + x^72 + w*x^71 + x^70 + x^69 + x^67 + x^65 + x^64 + w*x^63 + w*x^62 + x^61 + w*x^60 + w*x^59 + x^58 + x^55 + w^2*x^54 + w*x^53 + w^2*x^52 + w^2*x^51 + w^2*x^50 + w*x^49 + w^2*x^48 + w*x^47 + x^45 + x^44 + x^43 + 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 1 1 1 0 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 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 0 0 0 1 1 1 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1]
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[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 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 0 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 0 0 0 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 0 1 1]
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