MinT - Information on Result #1020702

Information on Result #1020702

Linear OOA(3¹⁹⁴, 72, F₃, 3, 116) (dual of [(72, 3), 22, 117]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁵¹, 24, F₃, 3, 38) (dual of [(24, 3), 21, 39]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,33P) [i] based on function field F/F₃ with g(F) = 13 and N(F) ≥ 24, using
  - a function field by SÃ©mirat [i]
linear OOA(3⁷¹, 24, F₃, 3, 58) (dual of [(24, 3), 1, 59]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁷¹, 25, F₃, 3, 58) (dual of [(25, 3), 4, 59]-NRT-code), using
  - strength reduction [i] based on linear OOA(3⁷¹, 25, F₃, 3, 59) (dual of [(25, 3), 4, 60]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(3⁸, 4, F₃, 3, 8) (dual of [(4, 3), 4, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;4,3) [i]
      2. linear OOA(3⁵⁹, 21, F₃, 3, 50) (dual of [(21, 3), 4, 51]-NRT-code), using
        repeating each code word 3 times [i] based on linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;F,4P) [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(3⁷², 24, F₃, 3, 72) (dual of [(24, 3), 0, 73]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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