MinT - Information on Result #941976

Information on Result #941976

Linear OOA(4¹⁹⁰, 97, F₄, 2, 159) (dual of [(97, 2), 4, 160]-NRT-code), using juxtaposition based on

linear OOA(4⁸, 6, F₄, 2, 7) (dual of [(6, 2), 4, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁸, 9, F₄, 2, 7) (dual of [(9, 2), 10, 8]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,10P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
linear OOA(4¹⁷⁸, 91, F₄, 2, 151) (dual of [(91, 2), 4, 152]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4⁸, 6, F₄, 2, 7) (dual of [(6, 2), 4, 8]-NRT-code) (see above)
  2. linear OOA(4¹⁶⁶, 85, F₄, 2, 143) (dual of [(85, 2), 4, 144]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(16¹⁵, 17, F₁₆, 15) (dual of [17, 2, 16]-code or 17-arc in PG(14,16)), using
        extended Reedâ€“Solomon code RS_e(2,16) [i]
        Simplex code S(2,16) [i]
      2. linear OOA(4⁸, 5, F₄, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,4) [i]

Mode: Constructive and linear.

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