MinT - Information on Result #1010084

Information on Result #1010084

Linear OOA(2²¹⁵, 78, F₂, 3, 93) (dual of [(78, 3), 19, 94]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁹⁹, 39, F₂, 3, 46) (dual of [(39, 3), 18, 47]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁹⁹, 45, F₂, 3, 46) (dual of [(45, 3), 36, 47]-NRT-code), using
  - strength reduction [i] based on linear OOA(2⁹⁹, 45, F₂, 3, 47) (dual of [(45, 3), 36, 48]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OOA(4²⁷, 15, F₄, 3, 23) (dual of [(15, 3), 18, 24]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,21P) [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]
linear OOA(2¹¹⁶, 39, F₂, 3, 93) (dual of [(39, 3), 1, 94]-NRT-code), using
- strength reduction [i] based on linear OOA(2¹¹⁶, 39, F₂, 3, 116) (dual of [(39, 3), 1, 117]-NRT-code), using
  - dual of repetition NRT-code with length 39 [i]

Mode: Constructive and linear.

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