MinT - Information on Result #908628

Information on Result #908628

Linear OOA(2²⁵¹, 129, F₂, 2, 130) (dual of [(129, 2), 7, 131]-NRT-code), using juxtaposition based on

linear OOA(2²⁵, 16, F₂, 2, 15) (dual of [(16, 2), 7, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁰, 8, F₂, 2, 7) (dual of [(8, 2), 6, 8]-NRT-code), using
    - an explicit generator matrix by Edel [i]
  2. linear OOA(2¹⁵, 8, F₂, 2, 15) (dual of [(8, 2), 1, 16]-NRT-code), using
    - dual of repetition NRT-code with length 8 [i]
linear OOA(2²¹⁹, 113, F₂, 2, 114) (dual of [(113, 2), 7, 115]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2⁹, 8, F₂, 2, 6) (dual of [(8, 2), 7, 7]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2⁹, 9, F₂, 2, 6) (dual of [(9, 2), 9, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (3, 9, 9)-net over F₂, using
        a shift-net [i]
  2. linear OOA(2²⁰³, 105, F₂, 2, 107) (dual of [(105, 2), 7, 108]-NRT-code), using
    - repeating each code word 3 times [i] based on linear OOA(2⁶³, 35, F₂, 2, 35) (dual of [(35, 2), 7, 36]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(2²⁸, 17, F₂, 2, 17) (dual of [(17, 2), 6, 18]-NRT-code), using
        (u,Â u+v)-construction [i] based on
        linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code), using
        an explicit generator matrix by Edel [i]
        linear OOA(2¹⁷, 9, F₂, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
        dual of repetition NRT-code with length 9 [i]
        linear OOA(2³⁵, 18, F₂, 2, 35) (dual of [(18, 2), 1, 36]-NRT-code), using
        dual of repetition NRT-code with length 18 [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.