MinT - Information on Result #1771725

Information on Result #1771725

Digital (212, 243, 128240)-net over F₃, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴³, 128240, F₃, 4, 31) (dual of [(128240, 4), 512717, 32]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴³, 132863, F₃, 4, 31) (dual of [(132863, 4), 531209, 32]-NRT-code), using
- 3¹ times duplication [i] based on linear OOA(3²⁴², 132863, F₃, 4, 31) (dual of [(132863, 4), 531210, 32]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(3²⁴², 531452, F₃, 31) (dual of [531452, 531210, 32]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²⁴², 531454, F₃, 31) (dual of [531454, 531212, 32]-code), using
      - constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
        linear OA(3²⁴¹, 531441, F₃, 31) (dual of [531441, 531200, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
        linear OA(3²²⁹, 531441, F₃, 29) (dual of [531441, 531212, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(3¹, 13, F₃, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: Linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.