MinT - Information on Result #1025127

Information on Result #1025127

Linear OOA(2²⁰², 72, F₂, 3, 101) (dual of [(72, 3), 14, 102]-NRT-code), using juxtaposition based on

linear OOA(2⁸², 32, F₂, 3, 43) (dual of [(32, 3), 14, 44]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁸², 33, F₂, 3, 43) (dual of [(33, 3), 17, 44]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,55P) [i] based on function field F/F₂ with g(F) = 39 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁰⁶, 40, F₂, 3, 57) (dual of [(40, 3), 14, 58]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴⁷, 20, F₂, 3, 28) (dual of [(20, 3), 13, 29]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,31P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2⁵⁹, 20, F₂, 3, 57) (dual of [(20, 3), 1, 58]-NRT-code), using
    - strength reduction [i] based on linear OOA(2⁵⁹, 20, F₂, 3, 59) (dual of [(20, 3), 1, 60]-NRT-code), using
      - dual of repetition NRT-code with length 20 [i]

Mode: Constructive and linear.

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