MinT - Information on Result #906106

Information on Result #906106

Linear OOA(3¹⁵⁵, 84, F₃, 2, 89) (dual of [(84, 2), 13, 90]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁴⁴, 28, F₃, 2, 29) (dual of [(28, 2), 12, 30]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,26P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3⁵⁵, 28, F₃, 2, 44) (dual of [(28, 2), 1, 45]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁵⁵, 29, F₃, 2, 44) (dual of [(29, 2), 3, 45]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(3⁵, 4, F₃, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;3,3) [i]
    2. linear OOA(3⁴⁷, 25, F₃, 2, 38) (dual of [(25, 2), 3, 39]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(3⁵, 4, F₃, 2, 5) (dual of [(4, 2), 3, 6]-NRT-code) (see above)
        linear OOA(3³⁹, 21, F₃, 2, 32) (dual of [(21, 2), 3, 33]-NRT-code), using
        repeating each code word 3 times [i] based on linear OOA(3¹¹, 7, F₃, 2, 10) (dual of [(7, 2), 3, 11]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,3P) [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(3⁵⁶, 28, F₃, 2, 56) (dual of [(28, 2), 0, 57]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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