MinT - Information on Result #1025142

Information on Result #1025142

Linear OOA(2¹³⁷, 50, F₂, 3, 70) (dual of [(50, 3), 13, 71]-NRT-code), using juxtaposition based on

linear OOA(2³⁵, 16, F₂, 3, 20) (dual of [(16, 3), 13, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2³⁵, 17, F₂, 3, 20) (dual of [(17, 3), 16, 21]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,30P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]
linear OOA(2⁸⁹, 34, F₂, 3, 49) (dual of [(34, 3), 13, 50]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2³⁹, 17, F₂, 3, 24) (dual of [(17, 3), 12, 25]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,26P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17 (see above)
  2. linear OOA(2⁵⁰, 17, F₂, 3, 49) (dual of [(17, 3), 1, 50]-NRT-code), using
    - strength reduction [i] based on linear OOA(2⁵⁰, 17, F₂, 3, 50) (dual of [(17, 3), 1, 51]-NRT-code), using
      - dual of repetition NRT-code with length 17 [i]

Mode: Constructive and linear.

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