MinT - Information on Result #1054118

Information on Result #1054118

Linear OOA(2⁶⁵, 18, F₂, 4, 36) (dual of [(18, 4), 7, 37]-NRT-code), using OOA 2-folding based on linear OOA(2⁶⁵, 36, F₂, 2, 36) (dual of [(36, 2), 7, 37]-NRT-code), using

strength reduction [i] based on linear OOA(2⁶⁵, 36, F₂, 2, 37) (dual of [(36, 2), 7, 38]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2⁷, 7, F₂, 2, 5) (dual of [(7, 2), 7, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (2, 7, 7)-net over F₂, using
      - a shift-net [i]
  2. linear OOA(2⁵¹, 29, F₂, 2, 31) (dual of [(29, 2), 7, 32]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2⁵¹, 30, F₂, 2, 31) (dual of [(30, 2), 9, 32]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(8⁷, 10, F₈, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,8)), using
        Denniston code D(1,8) [i]
        linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.