MinT - Information on Result #909172

Information on Result #909172

Linear OOA(3¹⁶⁵, 85, F₃, 2, 112) (dual of [(85, 2), 5, 113]-NRT-code), using juxtaposition based on

linear OOA(3⁹, 7, F₃, 2, 8) (dual of [(7, 2), 5, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁵¹, 78, F₃, 2, 103) (dual of [(78, 2), 5, 104]-NRT-code), using
- repeating each code word 2 times [i] based on linear OOA(3⁷³, 39, F₃, 2, 51) (dual of [(39, 2), 5, 52]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(3²², 13, F₃, 2, 17) (dual of [(13, 2), 4, 18]-NRT-code), using
      - extracting embedded OOA [i] based on digital (5, 22, 13)-net over F₃, using
        net from sequence [i] based on digital (5, 12)-sequence over F₃, using
        Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 4, N(F)Â =Â 12, and 1 place with degree 2 [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(3²⁵, 13, F₃, 2, 25) (dual of [(13, 2), 1, 26]-NRT-code), using
      - dual of repetition NRT-code with length 13 [i]
    3. linear OOA(3²⁶, 13, F₃, 2, 26) (dual of [(13, 2), 0, 27]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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