MinT - Information on Result #1080678

Information on Result #1080678

Linear OOA(2²⁵⁴, 74, F₂, 4, 109) (dual of [(74, 4), 42, 110]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁰⁸, 42, F₂, 4, 54) (dual of [(42, 4), 60, 55]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,113P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁴⁶, 37, F₂, 4, 109) (dual of [(37, 4), 2, 110]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁴⁶, 38, F₂, 4, 109) (dual of [(38, 4), 6, 110]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2²⁶, 8, F₂, 4, 22) (dual of [(8, 4), 6, 23]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,9P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(2¹¹⁴, 30, F₂, 4, 86) (dual of [(30, 4), 6, 87]-NRT-code), using
      - repeating each code word 3 times [i] based on linear OOA(2³⁴, 10, F₂, 4, 28) (dual of [(10, 4), 6, 29]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,11P) [i] based on function field F/F₂ with g(F) = 6 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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