MinT - Information on Result #1009827

Information on Result #1009827

Linear OOA(2¹²⁶, 46, F₂, 3, 64) (dual of [(46, 3), 12, 65]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁵⁸, 23, F₂, 3, 32) (dual of [(23, 3), 11, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁵⁸, 24, F₂, 3, 32) (dual of [(24, 3), 14, 33]-NRT-code), using
  - strength reduction [i] based on linear OOA(2⁵⁸, 24, F₂, 3, 33) (dual of [(24, 3), 14, 34]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OOA(4¹⁷, 8, F₄, 3, 16) (dual of [(8, 3), 7, 17]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(4¹⁷, 9, F₄, 3, 16) (dual of [(9, 3), 10, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,10P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
        the Hermitian function field over F₄ [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(2⁶⁸, 23, F₂, 3, 64) (dual of [(23, 3), 1, 65]-NRT-code), using
- strength reduction [i] based on linear OOA(2⁶⁸, 23, F₂, 3, 68) (dual of [(23, 3), 1, 69]-NRT-code), using
  - dual of repetition NRT-code with length 23 [i]

Mode: Constructive and linear.

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