MinT - Information on Result #1080561

Information on Result #1080561

Linear OOA(2²¹⁷, 66, F₂, 4, 96) (dual of [(66, 4), 47, 97]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁸⁷, 33, F₂, 4, 48) (dual of [(33, 4), 45, 49]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,83P) [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(2¹³⁰, 33, F₂, 4, 96) (dual of [(33, 4), 2, 97]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹³⁰, 34, F₂, 4, 96) (dual of [(34, 4), 6, 97]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2¹⁸, 6, F₂, 4, 16) (dual of [(6, 4), 6, 17]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,7P) [i] based on function field F/F₂ with g(F) = 2 and N(F) ≥ 6, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(2¹⁰⁶, 28, F₂, 4, 79) (dual of [(28, 4), 6, 80]-NRT-code), using
      - repeating each code word 4 times [i] based on linear OOA(2²², 7, F₂, 4, 19) (dual of [(7, 4), 6, 20]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(4;F,8P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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