MinT - Information on Result #1025016

Information on Result #1025016

Linear OOA(2¹⁵⁶, 58, F₂, 3, 68) (dual of [(58, 3), 18, 69]-NRT-code), using juxtaposition based on

linear OOA(2³⁶, 18, F₂, 3, 18) (dual of [(18, 3), 18, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2³³, 17, F₂, 3, 18) (dual of [(17, 3), 18, 19]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,32P) [i] based on function field F/F₂ with g(F) = 15 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁰², 40, F₂, 3, 49) (dual of [(40, 3), 18, 50]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴³, 20, F₂, 3, 24) (dual of [(20, 3), 17, 25]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,35P) [i] based on function field F/F₂ with g(F) = 19 and N(F) ≥ 20, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2⁵⁹, 20, F₂, 3, 49) (dual of [(20, 3), 1, 50]-NRT-code), using
    - strength reduction [i] based on linear OOA(2⁵⁹, 20, F₂, 3, 59) (dual of [(20, 3), 1, 60]-NRT-code), using
      - dual of repetition NRT-code with length 20 [i]

Mode: Constructive and linear.

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