MinT - Information on Result #1067874

Information on Result #1067874

Linear OOA(3¹⁶⁸, 43, F₃, 4, 132) (dual of [(43, 4), 4, 133]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁶⁸, 86, F₃, 2, 132) (dual of [(86, 2), 4, 133]-NRT-code), using

strength reduction [i] based on linear OOA(3¹⁶⁸, 86, F₃, 2, 133) (dual of [(86, 2), 4, 134]-NRT-code), using
- juxtaposition [i] based on
  1. 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]
  2. linear OOA(3¹⁵⁶, 80, F₃, 2, 125) (dual of [(80, 2), 4, 126]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(9¹⁸, 20, F₉, 17) (dual of [20, 2, 18]-code), using
        repeating each code word 2 times [i] based on 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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.