MinT - Information on Result #1009863

Information on Result #1009863

Linear OOA(2¹⁴⁷, 54, F₂, 3, 69) (dual of [(54, 3), 15, 70]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁷, 27, F₂, 3, 34) (dual of [(27, 3), 14, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁶⁷, 29, F₂, 3, 34) (dual of [(29, 3), 20, 35]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2⁶⁸, 30, F₂, 3, 35) (dual of [(30, 3), 22, 36]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OOA(4¹⁹, 10, F₄, 3, 17) (dual of [(10, 3), 11, 18]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,12P) [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, 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(2⁸⁰, 27, F₂, 3, 69) (dual of [(27, 3), 1, 70]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁸⁰, 27, F₂, 3, 80) (dual of [(27, 3), 1, 81]-NRT-code), using
  - dual of repetition NRT-code with length 27 [i]

Mode: Constructive and linear.

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