MinT - Information on Result #941736

Information on Result #941736

Linear OOA(3⁹⁸, 51, F₃, 2, 76) (dual of [(51, 2), 4, 77]-NRT-code), using juxtaposition based on

linear OOA(3⁸, 6, F₃, 2, 7) (dual of [(6, 2), 4, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁸, 7, F₃, 2, 7) (dual of [(7, 2), 6, 8]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3⁸⁶, 45, F₃, 2, 68) (dual of [(45, 2), 4, 69]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3⁶, 5, F₃, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁶, 6, F₃, 2, 5) (dual of [(6, 2), 6, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(3⁶, 12, F₃, 5) (dual of [12, 6, 6]-code), using
        extended Golay code G_e(3) [i]
  2. linear OOA(3⁷⁶, 40, F₃, 2, 62) (dual of [(40, 2), 4, 63]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(9⁸, 10, F₉, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
        extended Reedâ€“Solomon code RS_e(2,9) [i]
        Simplex code S(2,9) [i]
      2. linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [i]

Mode: Constructive and linear.

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