MinT - Information on Result #909123

Information on Result #909123

Linear OOA(3⁹⁶, 51, F₃, 2, 65) (dual of [(51, 2), 6, 66]-NRT-code), using juxtaposition based on

linear OOA(3¹⁸, 12, F₃, 2, 14) (dual of [(12, 2), 6, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₃ with g(F) = 4 and N(F) ≥ 12, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3⁷², 39, F₃, 2, 50) (dual of [(39, 2), 6, 51]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3²¹, 13, F₃, 2, 16) (dual of [(13, 2), 5, 17]-NRT-code), using
    - extracting embedded OOA [i] based on digital (5, 21, 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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