MinT - Information on Result #1011184

Information on Result #1011184

Linear OOA(3¹⁴⁹, 62, F₃, 3, 72) (dual of [(62, 3), 37, 73]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁵⁷, 32, F₃, 3, 36) (dual of [(32, 3), 39, 37]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,59P) [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3⁹², 31, F₃, 3, 72) (dual of [(31, 3), 1, 73]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁹², 32, F₃, 3, 72) (dual of [(32, 3), 4, 73]-NRT-code), using
  - strength reduction [i] based on linear OOA(3⁹², 32, F₃, 3, 76) (dual of [(32, 3), 4, 77]-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(3⁸⁰, 28, F₃, 3, 67) (dual of [(28, 3), 4, 68]-NRT-code), using
        repeating each code word 4 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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