MinT - Information on Result #1011509

Information on Result #1011509

Linear OOA(3²¹⁴, 84, F₃, 3, 101) (dual of [(84, 3), 38, 102]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁸⁹, 42, F₃, 3, 50) (dual of [(42, 3), 37, 51]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,75P) [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, 101) (dual of [(42, 3), 1, 102]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹²⁵, 43, F₃, 3, 101) (dual of [(43, 3), 4, 102]-NRT-code), using
  - strength reduction [i] based on linear OOA(3¹²⁵, 43, F₃, 3, 102) (dual of [(43, 3), 4, 103]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3⁸, 4, F₃, 3, 8) (dual of [(4, 3), 4, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;4,3) [i]
      2. linear OOA(3¹¹³, 39, F₃, 3, 93) (dual of [(39, 3), 4, 94]-NRT-code), using
        juxtaposition [i] based on
        linear OOA(3⁸, 4, F₃, 3, 8) (dual of [(4, 3), 4, 9]-NRT-code) (see above)
        linear OOA(3¹⁰¹, 35, F₃, 3, 84) (dual of [(35, 3), 4, 85]-NRT-code), using
        repeating each code word 5 times [i] based on 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]

Mode: Constructive and linear.

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