Bounds on the minimum distance of additive quantum codes

Bounds on [[106,3]]2

lower bound:22
upper bound:35

Construction

Construction of a [[106,3,22]] quantum code:
[1]:  [[109, 1, 25]] quantum code over GF(2^2)
     cyclic code of length 109 with generating polynomial x^55 + w^2*x^54 + w*x^53 + w^2*x^52 + w^2*x^51 + w^2*x^50 + w*x^48 + x^47 + w*x^46 + x^44 + w*x^42 + x^41 + w^2*x^40 + x^39 + w*x^38 + x^36 + x^35 + w*x^33 + x^32 + w^2*x^31 + w^2*x^30 + x^29 + x^26 + w^2*x^25 + w^2*x^24 + x^23 + w*x^22 + x^20 + x^19 + w*x^17 + x^16 + w^2*x^15 + x^14 + w*x^13 + x^11 + w*x^9 + x^8 + w*x^7 + w^2*x^5 + w^2*x^4 + w^2*x^3 + w*x^2 + w^2*x + 1
[2]:  [[106, 4, 22]] quantum code over GF(2^2)
     Shortening of the stabilizer code of [1] at { 107 .. 109 }
[3]:  [[106, 3, 22]] quantum code over GF(2^2)
     Subcode of [2]

    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 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 1 0 0 1 1 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 1 1 0 1 0 0 1 1 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 0 1 1 0 1 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 1 1 0 1 0 1 1 0 0 1 0 1 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 0 0 0]
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last modified: 2020-07-26

Notes


This page is maintained by Markus Grassl (codes@codetables.de). Last change: 23.10.2014