MinT - Information on Result #1011316

Information on Result #1011316

Linear OOA(3¹⁷¹, 70, F₃, 3, 82) (dual of [(70, 3), 39, 83]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁶⁷, 36, F₃, 3, 41) (dual of [(36, 3), 41, 42]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,66P) [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using
  - an explicitly constructive algebraic function field [i]
- algebraic-geometric NRT-code AG(3;F,33P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
linear OOA(3¹⁰⁴, 35, F₃, 3, 82) (dual of [(35, 3), 1, 83]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁰⁴, 36, F₃, 3, 82) (dual of [(36, 3), 4, 83]-NRT-code), using
  - strength reduction [i] based on linear OOA(3¹⁰⁴, 36, F₃, 3, 83) (dual of [(36, 3), 4, 84]-NRT-code), using
    - repeating each code word 6 times [i] based on linear OOA(3¹⁴, 6, F₃, 3, 13) (dual of [(6, 3), 4, 14]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(3¹⁴, 7, F₃, 3, 13) (dual of [(7, 3), 7, 14]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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