MinT - Information on Result #909714

Information on Result #909714

Linear OOA(4¹⁶⁹, 87, F₄, 2, 128) (dual of [(87, 2), 5, 129]-NRT-code), using juxtaposition based on

linear OOA(4⁹, 7, F₄, 2, 8) (dual of [(7, 2), 5, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4⁹, 9, F₄, 2, 8) (dual of [(9, 2), 9, 9]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
linear OOA(4¹⁵⁵, 80, F₄, 2, 119) (dual of [(80, 2), 5, 120]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4³⁶, 20, F₄, 2, 29) (dual of [(20, 2), 4, 30]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4³⁶, 21, F₄, 2, 29) (dual of [(21, 2), 6, 30]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,12P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
        an explicitly constructive algebraic function field [i]
  2. linear OOA(4³⁹, 20, F₄, 2, 39) (dual of [(20, 2), 1, 40]-NRT-code), using
    - dual of repetition NRT-code with length 20 [i]
  3. linear OOA(4⁴⁰, 20, F₄, 2, 40) (dual of [(20, 2), 0, 41]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4⁴⁰, 20, F₄, 2, 40) (dual of [(20, 2), 0, 41]-NRT-code) (see above)

Mode: Constructive and linear.

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