Bounds on the minimum distance of additive quantum codes
Bounds on [[127,93]]2
| lower bound: | 7 |
| upper bound: | 10 |
Construction
Construction type: EzermanGrasslLingOzbudakOzkaya
Construction of a [[127,93,7]] quantum code:
[1]: [126, 17] Quasicyclic of degree 2 Linear Code over GF(2^2)
QuasiCyclicCode of length 126 with generating polynomials: x^46 + w*x^45 + w^2*x^44 + x^41 + w^2*x^40 + w^2*x^39 + x^37 + w*x^36 + x^35 + w^2*x^33 + x^32 + w*x^31 + w^2*x^29 + w*x^28 + w^2*x^27 + w^2*x^26 + w^2*x^25 + w^2*x^21 + w^2*x^19 + x^18 + x^17 + w*x^16 + w^2*x^14 + w*x^12 + w^2*x^11 + w*x^10 + w*x^9 + x^8 + x^7 + w*x^6 + w*x^5 + x^4 + w^2*x^3 + x^2 + w^2*x + 1, w*x^61 + w*x^60 + w*x^59 + x^58 + w*x^57 + x^55 + w*x^54 + w*x^53 + w^2*x^52 + w*x^50 + w^2*x^49 + x^48 + w^2*x^47 + w^2*x^46 + w*x^45 + x^44 + w^2*x^43 + w*x^42 + w^2*x^41 + w*x^40 + w^2*x^39 + w*x^38 + w^2*x^37 + w^2*x^36 + w^2*x^35 + w*x^34 + w^2*x^33 + w*x^32 + w*x^30 + w*x^29 + w^2*x^27 + w^2*x^26 + w*x^25 + w^2*x^24 + w^2*x^23 + x^22 + w*x^21 + w*x^20 + w^2*x^18 + w^2*x^16 + x^15 + w^2*x^14 + x^13 + w^2*x^12 + w^2*x^11 + x^9 + x^8 + w*x^6 + w^2*x^5 + x^4 + 1
[2]: [[127, 93, 7]] quantum code over GF(2^2)
QuantumConstructionX applied to [1] with e = 1
stabilizer matrix:
[1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 1 0 0 1 0 0 1 1 1 0 1 0 0 0 1 1 1 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 0 0 0 0 0 1 0 1 1 1 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 1 0 1 0 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 1]
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last modified: 2025-04-15
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