MinT - Information on Result #909120

Information on Result #909120

Linear OOA(3⁸⁴, 45, F₃, 2, 57) (dual of [(45, 2), 6, 58]-NRT-code), using juxtaposition based on

linear OOA(3¹², 9, F₃, 2, 9) (dual of [(9, 2), 6, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹², 10, F₃, 2, 9) (dual of [(10, 2), 8, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,10P) [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(3⁶⁶, 36, F₃, 2, 47) (dual of [(36, 2), 6, 48]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3¹⁹, 12, F₃, 2, 15) (dual of [(12, 2), 5, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,8P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(3²³, 12, F₃, 2, 23) (dual of [(12, 2), 1, 24]-NRT-code), using
    - dual of repetition NRT-code with length 12 [i]
  3. linear OOA(3²⁴, 12, F₃, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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