MinT - Information on Result #1049553

Information on Result #1049553

Linear OOA(3¹⁴⁹, 51, F₃, 3, 123) (dual of [(51, 3), 4, 124]-NRT-code), using juxtaposition 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]
linear OOA(3¹³¹, 45, F₃, 3, 109) (dual of [(45, 3), 4, 110]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(3¹¹, 5, F₃, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3¹¹, 7, F₃, 3, 10) (dual of [(7, 3), 10, 11]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,10P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7 (see above)
  2. linear OOA(3¹¹⁶, 40, F₃, 3, 98) (dual of [(40, 3), 4, 99]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. 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(3¹⁰, 4, F₃, 3, 10) (dual of [(4, 3), 2, 11]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;2,3) [i]

Mode: Constructive and linear.

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