MinT - Information on Result #909442

Information on Result #909442

Linear OOA(4¹⁹¹, 101, F₄, 2, 127) (dual of [(101, 2), 11, 128]-NRT-code), using juxtaposition based on

linear OOA(4²⁹, 20, F₄, 2, 22) (dual of [(20, 2), 11, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4²⁹, 21, F₄, 2, 22) (dual of [(21, 2), 13, 23]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,19P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4¹⁵¹, 81, F₄, 2, 104) (dual of [(81, 2), 11, 105]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4⁴⁴, 27, F₄, 2, 34) (dual of [(27, 2), 10, 35]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,19P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4⁵³, 27, F₄, 2, 52) (dual of [(27, 2), 1, 53]-NRT-code), using
    - strength reduction [i] based on linear OOA(4⁵³, 27, F₄, 2, 53) (dual of [(27, 2), 1, 54]-NRT-code), using
      - dual of repetition NRT-code with length 27 [i]
  3. linear OOA(4⁵⁴, 27, F₄, 2, 54) (dual of [(27, 2), 0, 55]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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