MinT - Information on Result #908622

Information on Result #908622

Linear OOA(2¹⁸⁹, 98, F₂, 2, 98) (dual of [(98, 2), 7, 99]-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(2¹⁵⁷, 82, F₂, 2, 82) (dual of [(82, 2), 7, 83]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹⁷, 12, F₂, 2, 10) (dual of [(12, 2), 7, 11]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2¹⁷, 13, F₂, 2, 10) (dual of [(13, 2), 9, 11]-NRT-code), using
      - extracting embedded OOA [i] based on digital (7, 17, 13)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2¹³³, 70, F₂, 2, 71) (dual of [(70, 2), 7, 72]-NRT-code), using
    - repeating each code word 2 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.