MinT - Information on Result #1011526

Information on Result #1011526

Linear OOA(3²¹⁵, 84, F₃, 3, 103) (dual of [(84, 3), 37, 104]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁹⁰, 42, F₃, 3, 51) (dual of [(42, 3), 36, 52]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,74P) [i] based on function field F/F₃ with g(F) = 39 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹²⁵, 42, F₃, 3, 103) (dual of [(42, 3), 1, 104]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹²⁵, 43, F₃, 3, 103) (dual of [(43, 3), 4, 104]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(3¹⁰⁴, 36, F₃, 3, 86) (dual of [(36, 3), 4, 87]-NRT-code), using
      - repeating each code word 3 times [i] based on linear OOA(3³², 12, F₃, 3, 28) (dual of [(12, 3), 4, 29]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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