MinT - Information on Result #909612

Information on Result #909612

Linear OOA(4²²⁸, 117, F₄, 2, 171) (dual of [(117, 2), 6, 172]-NRT-code), using juxtaposition based on

linear OOA(4⁶, 6, F₄, 2, 5) (dual of [(6, 2), 6, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4⁶, 12, F₄, 5) (dual of [12, 6, 6]-code), using
  - extended quadratic residue code Q_e(12,4) [i]
linear OOA(4²¹⁶, 111, F₄, 2, 165) (dual of [(111, 2), 6, 166]-NRT-code), using
- strength reduction [i] based on linear OOA(4²¹⁶, 111, F₄, 2, 173) (dual of [(111, 2), 6, 174]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(4³⁶, 21, F₄, 2, 29) (dual of [(21, 2), 6, 30]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,12P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(4¹⁷⁴, 90, F₄, 2, 143) (dual of [(90, 2), 6, 144]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(16¹⁵, 18, F₁₆, 15) (dual of [18, 3, 16]-code or 18-arc in PG(14,16)), using
        Denniston code D(1,16) [i]
        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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