MinT - Information on Result #909065

Information on Result #909065

Linear OOA(3¹⁷⁸, 93, F₃, 2, 112) (dual of [(93, 2), 8, 113]-NRT-code), using juxtaposition based on

linear OOA(3¹⁰, 9, F₃, 2, 7) (dual of [(9, 2), 8, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁰, 10, F₃, 2, 7) (dual of [(10, 2), 10, 8]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,12P) [i] based on function field F/F₃ with g(F) = 3 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁶⁰, 84, F₃, 2, 104) (dual of [(84, 2), 8, 105]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁴⁹, 28, F₃, 2, 34) (dual of [(28, 2), 7, 35]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,21P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3⁵⁵, 28, F₃, 2, 52) (dual of [(28, 2), 1, 53]-NRT-code), using
    - strength reduction [i] based on linear OOA(3⁵⁵, 28, F₃, 2, 55) (dual of [(28, 2), 1, 56]-NRT-code), using
      - dual of repetition NRT-code with length 28 [i]
  3. linear OOA(3⁵⁶, 28, F₃, 2, 56) (dual of [(28, 2), 0, 57]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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