MinT - Information on Result #1025434

Information on Result #1025434

Linear OOA(2²¹⁷, 75, F₂, 3, 125) (dual of [(75, 3), 8, 126]-NRT-code), using juxtaposition based on

linear OOA(2¹⁶, 8, F₂, 3, 12) (dual of [(8, 3), 8, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,11P) [i] based on function field F/F₂ with g(F) = 4 and N(F) ≥ 8, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁹³, 67, F₂, 3, 112) (dual of [(67, 3), 8, 113]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁹³, 69, F₂, 3, 112) (dual of [(69, 3), 14, 113]-NRT-code), using
  - 16 step truncation [i] based on linear OOA(2²⁰⁹, 75, F₂, 3, 128) (dual of [(75, 3), 16, 129]-NRT-code), using
    - strength reduction [i] based on linear OOA(2²⁰⁹, 75, F₂, 3, 131) (dual of [(75, 3), 16, 132]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(16¹¹, 15, F₁₆, 11) (dual of [15, 4, 12]-code or 15-arc in PG(10,16)), using
        discarding factors / shortening the dual code based on linear OA(16¹¹, 16, F₁₆, 11) (dual of [16, 5, 12]-code or 16-arc in PG(10,16)), using
        Reedâ€“Solomon code RS(5,16) [i]
        linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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