MinT - Information on Result #909617

Information on Result #909617

Linear OOA(4¹⁴⁶, 76, F₄, 2, 109) (dual of [(76, 2), 6, 110]-NRT-code), using juxtaposition based on

linear OOA(4¹⁰, 8, F₄, 2, 9) (dual of [(8, 2), 6, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁰, 9, F₄, 2, 9) (dual of [(9, 2), 8, 10]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,8P) [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(4¹³⁰, 68, F₄, 2, 99) (dual of [(68, 2), 6, 100]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4²⁹, 17, F₄, 2, 24) (dual of [(17, 2), 5, 25]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,9P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4³³, 17, F₄, 2, 33) (dual of [(17, 2), 1, 34]-NRT-code), using
    - dual of repetition NRT-code with length 17 [i]
  3. linear OOA(4³⁴, 17, F₄, 2, 34) (dual of [(17, 2), 0, 35]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4³⁴, 17, F₄, 2, 34) (dual of [(17, 2), 0, 35]-NRT-code) (see above)

Mode: Constructive and linear.

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