MinT - Information on Result #895857

Information on Result #895857

Linear OOA(4⁶⁵, 42, F₄, 2, 35) (dual of [(42, 2), 19, 36]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4²⁴, 21, F₄, 2, 17) (dual of [(21, 2), 18, 18]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,24P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4⁴¹, 21, F₄, 2, 35) (dual of [(21, 2), 1, 36]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁴¹, 22, F₄, 2, 35) (dual of [(22, 2), 3, 36]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4⁵, 4, F₄, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;3,4) [i]
    2. linear OOA(4³³, 18, F₄, 2, 29) (dual of [(18, 2), 3, 30]-NRT-code), using
      - repeating each code word 2 times [i] based on linear OOA(4¹⁵, 9, F₄, 2, 14) (dual of [(9, 2), 3, 15]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,3P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [i]

Mode: Constructive and linear.

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