Bounds on the minimum distance of additive quantum codes

Bounds on [[95,77]]₂

lower bound:	4
upper bound:	6
Construction

Construction of a [[95,77,4]] quantum code:
[1]:  [[95, 77, 4]] quantum code over GF(2^2)
     QuasiCyclicCode of length 95 with generating polynomials: w*x^18 + w^2*x^16 + w*x^13 + w^2*x^12 + x^11 + w*x^9 + w^2*x^8 + w^2*x^7 + w*x^6 + w^2*x^5 + w*x^4 + w*x^3 + w,  w^2*x^17 + x^14 + w*x^12 + w^2*x^11 + x^9 + w^2*x^8 + w^2*x^6 + w*x^5 + x^4 + w^2*x^2 + w*x,  w*x^18 + w^2*x^17 + w^2*x^13 + w^2*x^12 + w*x^9 + w^2*x^8 + w^2*x^7 + x^6 + w*x^5 + w*x^4 + w^2*x^3 + w*x + w^2,  w^2*x^16 + w*x^14 + x^13 + w*x^12 + w^2*x^11 + x^10 + x^9 + w*x^8 + w*x^7 + w^2*x^6 + w^2*x^5 + x^2,  x^17 + w*x^16 + w^2*x^15 + w^2*x^14 + w*x^13 + x^11 + x^10 + x^7 + x^6 + w*x^5 + w*x^4 + w*x^3 + x^2 + x + w^2

    stabilizer matrix:

      [1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 1 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 1 1 1 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0|1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0]
      [0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 0 1 0 0 0 0 0 0 1 1 1 0 0 1 0 1 1 0 1 0 1 1 1 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 1 1 0 1 1 1 1 1 0 1 0|0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 1 0 0 1 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 0 0 0 1|0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 1 0 1 0 1 0 1 1 1 1 1 1 1 1 0 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0]
      [0 0 1 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1|0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 0 0 1 1 0 0 1 1 0 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 1 1 0 0 0 1 1]
      [0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 1 1 0 0 1 0 0 0 1 0 0 0 0 0 1 1 0 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0|0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 0 1 0 0]
      [0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 1 0 1|0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 0 0 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 1 0 1 1 1 0 1 1 1 1 1]
      [0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 0 0 1 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 1 0 0 0 1 1 0 0 0 1 1 0 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0 0 1|0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 0 1 1 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 0 1 0 0]
      [0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1]
      [0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 0 1 1 0 1 0 1 0|0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 1 0 0 1 1 1 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 1 0 1 0 0]
      [0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0|0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1 1]
      [0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 1 0 1 0 1 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 0 1 1 0 1 1 0 0 1 0 1 1|0 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 1 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0]
      [0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 1 1 1 0 1 1 0 1 0 0 1 0 0 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 1 1 1 0 0 0 0 0 1|0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 1 1 1 1 0 0 1 1 1 0 0 1 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 0 1 0 1]
      [0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1 1|0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 0 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0 1]
      [0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0|0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 1 1 1 1 1 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 1 1 1 1 0 0 1 1 0 0 1 1 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 0 1 0 1 1 0 1 0 0 1 0 1 1 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 0 0 0 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0 0 0 0 1 1 0 1|0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 0 0 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 0]
      [0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0 0|0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 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 0 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 1 1 1 1 0 1 0 0 1 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 1 0 1 1 1 1 1 1 0 0|0 0 0 0 0 0 0 0 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 1 0 1 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 1 1 0 1 0 1 1 1 0 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 1 1 1 1 0 0 0 0]

last modified: 2006-04-03
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 even 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: 23.10.2014
Bounds on the minimum distance of additive quantum codes

Bounds on [[95,77]]2

Construction

Notes

Bounds on [[95,77]]₂
