MinT - Information on Result #909159

Information on Result #909159

Linear OOA(3²¹⁷, 111, F₃, 2, 147) (dual of [(111, 2), 5, 148]-NRT-code), using juxtaposition based on

linear OOA(3⁷, 6, F₃, 2, 6) (dual of [(6, 2), 5, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁷, 7, F₃, 2, 6) (dual of [(7, 2), 7, 7]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;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(3²⁰⁵, 105, F₃, 2, 140) (dual of [(105, 2), 5, 141]-NRT-code), using
- repeating each code word 3 times [i] based on linear OOA(3⁶⁵, 35, F₃, 2, 46) (dual of [(35, 2), 5, 47]-NRT-code), using
  - 9 step truncation [i] based on linear OOA(3⁷⁴, 40, F₃, 2, 55) (dual of [(40, 2), 6, 56]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(9⁷, 10, F₉, 7) (dual of [10, 3, 8]-code or 10-arc in PG(6,9)), using
        extended Reedâ€“Solomon code RS_e(3,9) [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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