MinT - Information on Result #906358

Information on Result #906358

Linear OOA(4⁷⁹, 45, F₄, 2, 50) (dual of [(45, 2), 11, 51]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(4²⁰, 15, F₄, 2, 16) (dual of [(15, 2), 10, 17]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,13P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4²⁹, 15, F₄, 2, 25) (dual of [(15, 2), 1, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4²⁹, 16, F₄, 2, 25) (dual of [(16, 2), 3, 26]-NRT-code), using
  - repeating each code word 2 times [i] based on linear OOA(4¹³, 8, F₄, 2, 12) (dual of [(8, 2), 3, 13]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹³, 9, F₄, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,5P) [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(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]

Mode: Constructive and linear.

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