MinT - Information on Result #1025334

Information on Result #1025334

Linear OOA(2¹³⁵, 48, F₂, 3, 76) (dual of [(48, 3), 9, 77]-NRT-code), using juxtaposition based on

linear OOA(2¹⁸, 9, F₂, 3, 13) (dual of [(9, 3), 9, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁰⁸, 39, F₂, 3, 62) (dual of [(39, 3), 9, 63]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁰⁸, 41, F₂, 3, 62) (dual of [(41, 3), 15, 63]-NRT-code), using
  - 2 step truncation [i] based on linear OOA(2¹¹⁰, 42, F₂, 3, 64) (dual of [(42, 3), 16, 65]-NRT-code), using
    - strength reduction [i] based on linear OOA(2¹¹⁰, 42, F₂, 3, 65) (dual of [(42, 3), 16, 66]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(16¹⁰, 14, F₁₆, 10) (dual of [14, 4, 11]-code or 14-arc in PG(9,16)), using
        discarding factors / shortening the dual code based on linear OA(16¹⁰, 16, F₁₆, 10) (dual of [16, 6, 11]-code or 16-arc in PG(9,16)), using
        Reedâ€“Solomon code RS(6,16) [i]
        linear OOA(2⁵, 3, F₂, 3, 5) (dual of [(3, 3), 4, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;4,2) [i]

Mode: Constructive and linear.

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