MinT - Information on Result #941767

Information on Result #941767

Linear OOA(3¹⁷⁴, 89, F₃, 2, 137) (dual of [(89, 2), 4, 138]-NRT-code), using juxtaposition based on

linear OOA(3¹⁴, 9, F₃, 2, 11) (dual of [(9, 2), 4, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁴, 10, F₃, 2, 11) (dual of [(10, 2), 6, 12]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,8P) [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(3¹⁵⁶, 80, F₃, 2, 125) (dual of [(80, 2), 4, 126]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(9¹⁸, 20, F₉, 17) (dual of [20, 2, 18]-code), using
    - repeating each code word 2 times [i] based on linear OA(9⁸, 10, F₉, 8) (dual of [10, 2, 9]-code or 10-arc in PG(7,9)), using
      - extended Reedâ€“Solomon code RS_e(2,9) [i]
      - Simplex code S(2,9) [i]
  2. linear OOA(3⁶, 4, F₃, 2, 6) (dual of [(4, 2), 2, 7]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;2,3) [i]

Mode: Constructive and linear.

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