Bounds on the minimum distance of additive quantum codes

Bounds on [[44,8]]₂

Construction

Construction of a [[44,8,10]] quantum code:
[1]:  [[44, 44, 10]] quantum code over GF(2^2)
     QuasiCyclicCode of length 44 stacked to height  2 with generating polynomials: x^4 + w^2*x^3 + w*x^2 + x + w,  w*x^18 + w^2*x^17 + w^2*x^14 + x^13 + w^2*x^12 + w*x^11 + w*x^10 + w^2*x^9 + x^7 + w*x^6 + x^5 + w*x^3 + w^2*x^2 + x + w^2,  0,  x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1

    stabilizer matrix:


last modified: 2005-06-30

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.