Bounds on the minimum distance of additive quantum codes
Bounds on [[93,0]]2
| lower bound: | 22 |
| upper bound: | 32 |
Construction
Construction type: SeneviratneGarciaJarrahySamoylov
Construction of a [[93,0,22]] quantum code:
[1]: [[93, 0, 22]] self-dual quantum code over GF(2^2)
QuasiCyclicCode of length 93 stacked to height 4 with generating polynomials: w*x^28 + w*x^24 + w*x^22 + w*x^14 + w*x^12 + w*x^10 + w*x^8 + w*x^7 + w*x^6 + w*x^5 + w*x^4 + w*x + w^2, w*x^30 + w*x^28 + w*x^27 + w*x^26 + w*x^25 + w*x^23 + w*x^22 + w*x^21 + w*x^19 + w*x^17 + w*x^14 + w*x^12 + w*x^10 + w*x^9 + w*x^8 + w*x^6 + w*x^5 + w*x^4 + w*x^3 + w*x, w*x^30 + w*x^27 + w*x^26 + w*x^25 + w*x^24 + w*x^23 + w*x^21 + w*x^19 + w*x^17 + w*x^9 + w*x^7 + w*x^3 + w^2, w*x^29 + w*x^24 + w*x^20 + w*x^18 + w*x^16 + w*x^15 + w*x^13 + w*x^11 + w*x^7 + w*x^2 + w, w*x^29 + w*x^28 + w*x^22 + w*x^20 + w*x^18 + w*x^16 + w*x^15 + w*x^14 + w*x^13 + w*x^12 + w*x^11 + w*x^10 + w*x^8 + w*x^6 + w*x^5 + w*x^4 + w*x^2 + w*x + 1, w*x^30 + w*x^29 + w*x^27 + w*x^26 + w*x^25 + w*x^23 + w*x^21 + w*x^20 + w*x^19 + w*x^18 + w*x^17 + w*x^16 + w*x^15 + w*x^13 + w*x^11 + w*x^9 + w*x^3 + w*x^2 + 1, w*x^29 + w*x^26 + w*x^25 + w*x^24 + w*x^20 + w*x^18 + w*x^17 + w*x^16 + w*x^13 + w*x^11 + w*x^6 + w*x^2 + w, w*x^30 + w*x^26 + w*x^21 + w*x^19 + w*x^16 + w*x^15 + w*x^14 + w*x^12 + w*x^8 + w*x^7 + w*x^6 + w*x^3 + w*x, w*x^28 + w*x^26 + w*x^23 + w*x^22 + w*x^20 + w*x^18 + w*x^17 + w*x^16 + w*x^15 + w*x^14 + w*x^12 + w*x^10 + w*x^9 + w*x^6 + w*x^4 + x + 1, w*x^30 + w*x^29 + w*x^28 + w*x^27 + w*x^26 + w*x^25 + w*x^24 + w*x^23 + w*x^22 + w*x^21 + w*x^20 + w*x^19 + w*x^18 + w*x^17 + w*x^16 + w*x^15 + w*x^14 + w*x^13 + w*x^12 + w*x^11 + w*x^10 + w*x^9 + w*x^8 + w*x^7 + w*x^6 + w*x^5 + w*x^4 + w*x^3 + w*x^2 + w*x + w, w*x^30 + w*x^29 + w*x^28 + w*x^27 + w*x^26 + w*x^25 + w*x^24 + w*x^23 + w*x^22 + w*x^21 + w*x^20 + w*x^19 + w*x^18 + w*x^17 + w*x^16 + w*x^15 + w*x^14 + w*x^13 + w*x^12 + w*x^11 + w*x^10 + w*x^9 + w*x^8 + w*x^7 + w*x^6 + w*x^5 + w*x^4 + w*x^3 + w*x^2 + w*x + w, w*x^30 + w*x^29 + w*x^28 + w*x^27 + w*x^26 + w*x^25 + w*x^24 + w*x^23 + w*x^22 + w*x^21 + w*x^20 + w*x^19 + w*x^18 + w*x^17 + w*x^16 + w*x^15 + w*x^14 + w*x^13 + w*x^12 + w*x^11 + w*x^10 + w*x^9 + w*x^8 + w*x^7 + w*x^6 + w*x^5 + w*x^4 + w*x^3 + w*x^2 + w*x + w
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 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 1 1 1 0 1 0 0 1 0 1 1 1 1 1 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 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 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 1 1 1 1 1 1 1 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 0 0 1 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0]
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last modified: 2024-08-29
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