MinT - Information on Result #909579

Information on Result #909579

Linear OOA(4¹³⁹, 73, F₄, 2, 100) (dual of [(73, 2), 7, 101]-NRT-code), using juxtaposition based on

linear OOA(4¹⁹, 13, F₄, 2, 16) (dual of [(13, 2), 7, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁹, 14, F₄, 2, 16) (dual of [(14, 2), 9, 17]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,11P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4¹¹³, 60, F₄, 2, 83) (dual of [(60, 2), 7, 84]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4²⁴, 15, F₄, 2, 20) (dual of [(15, 2), 6, 21]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4²⁹, 15, F₄, 2, 27) (dual of [(15, 2), 1, 28]-NRT-code), using
    - strength reduction [i] based on linear OOA(4²⁹, 15, F₄, 2, 29) (dual of [(15, 2), 1, 30]-NRT-code), using
      - dual of repetition NRT-code with length 15 [i]
  3. linear OOA(4³⁰, 15, F₄, 2, 30) (dual of [(15, 2), 0, 31]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4³⁰, 15, F₄, 2, 30) (dual of [(15, 2), 0, 31]-NRT-code) (see above)

Mode: Constructive and linear.

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