MinT - Information on Result #906273

Information on Result #906273

Linear OOA(4¹¹⁰, 68, F₄, 2, 59) (dual of [(68, 2), 26, 60]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(4¹⁹, 17, F₄, 2, 14) (dual of [(17, 2), 15, 15]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,19P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4²⁴, 17, F₄, 2, 19) (dual of [(17, 2), 10, 20]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,14P) [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17 (see above)
linear OOA(4³³, 17, F₄, 2, 29) (dual of [(17, 2), 1, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4³³, 18, F₄, 2, 29) (dual of [(18, 2), 3, 30]-NRT-code), using
  - repeating each code word 2 times [i] based on linear OOA(4¹⁵, 9, F₄, 2, 14) (dual of [(9, 2), 3, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,3P) [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(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]

Mode: Constructive and linear.

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