MinT - Information on Result #1025035

Information on Result #1025035

Linear OOA(2¹⁵¹, 56, F₂, 3, 68) (dual of [(56, 3), 17, 69]-NRT-code), using juxtaposition based on

linear OOA(2³⁴, 17, F₂, 3, 19) (dual of [(17, 3), 17, 20]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,31P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁰⁰, 39, F₂, 3, 48) (dual of [(39, 3), 17, 49]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁰⁰, 44, F₂, 3, 48) (dual of [(44, 3), 32, 49]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2¹⁰¹, 45, F₂, 3, 49) (dual of [(45, 3), 34, 50]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OOA(4²⁸, 15, F₄, 3, 24) (dual of [(15, 3), 17, 25]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,20P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, 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]

Mode: Constructive and linear.

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