Bounds on the minimum distance of additive quantum codes
Bounds on [[137,0]]2
| lower bound: | 21 |
| upper bound: | 40 |
Construction
Construction of a [[137,0,21]] quantum code:
[1]: [137, 69, 21] Cyclic Linear Code over GF(2)
cyclic code of length 137 with generating polynomial x^68 + x^66 + x^65 + x^64 + x^62 + x^59 + x^58 + x^57 + x^55 + x^54 + x^51 + x^48 + x^47 + x^46 + x^43 + x^42 + x^40 + x^39 + x^37 + x^34 + x^31 + x^29 + x^28 + x^26 + x^25 + x^22 + x^21 + x^20 + x^17 + x^14 + x^13 + x^11 + x^10 + x^9 + x^6 + x^4 + x^3 + x^2 + 1
[2]: [138, 69, 22] Linear Code over GF(2)
ExtendCode [1] by 1
[3]: [[138, 0, 22]] CSS self-dual quantum code over GF(2^2)
CSS code using [2] and [2]
[4]: [[137, 0, 21]] self-dual quantum code over GF(2^2)
Puncturing of [3] at { 138 }
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 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 1 0 1 1 1 0 1 1 1 1 0 1 1 0 1 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 0 1 1 0 1 1 1 1 0 1 1 1 0 1 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 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 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]
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last modified: 2022-08-08
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.
This page is maintained by
Markus Grassl
(codes@codetables.de).
Last change: 10.06.2024