MinT - Information on Result #1010157

Information on Result #1010157

Linear OOA(2²⁰⁸, 74, F₂, 3, 101) (dual of [(74, 3), 14, 102]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁹⁸, 37, F₂, 3, 50) (dual of [(37, 3), 13, 51]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁹⁸, 42, F₂, 3, 50) (dual of [(42, 3), 28, 51]-NRT-code), using
  - strength reduction [i] based on linear OOA(2⁹⁸, 42, F₂, 3, 51) (dual of [(42, 3), 28, 52]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OOA(4²⁸, 14, F₄, 3, 25) (dual of [(14, 3), 14, 26]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,16P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]
      2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OOA(2¹¹⁰, 37, F₂, 3, 101) (dual of [(37, 3), 1, 102]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹¹⁰, 37, F₂, 3, 110) (dual of [(37, 3), 1, 111]-NRT-code), using
  - dual of repetition NRT-code with length 37 [i]

Mode: Constructive and linear.

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