MinT - Information on Result #1025511

Information on Result #1025511

Linear OOA(2¹³¹, 46, F₂, 3, 80) (dual of [(46, 3), 7, 81]-NRT-code), using juxtaposition based on

linear OOA(2¹⁴, 7, F₂, 3, 11) (dual of [(7, 3), 7, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,9P) [i] based on function field F/F₂ with g(F) = 3 and N(F) ≥ 7, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹¹⁰, 39, F₂, 3, 68) (dual of [(39, 3), 7, 69]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹¹⁰, 40, F₂, 3, 68) (dual of [(40, 3), 10, 69]-NRT-code), using
  - strength reduction [i] based on linear OOA(2¹¹⁰, 40, F₂, 3, 69) (dual of [(40, 3), 10, 70]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(32⁶, 8, F₃₂, 6) (dual of [8, 2, 7]-code or 8-arc in PG(5,32)), using
        discarding factors / shortening the dual code based on linear OA(32⁶, 32, F₃₂, 6) (dual of [32, 26, 7]-code or 32-arc in PG(5,32)), using
        Reedâ€“Solomon code RS(26,32) [i]
      2. linear OOA(2¹⁰, 5, F₂, 3, 9) (dual of [(5, 3), 5, 10]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,5P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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