MinT - Information on Result #1010363

Information on Result #1010363

Linear OOA(2²⁵⁷, 89, F₂, 3, 135) (dual of [(89, 3), 10, 136]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹²², 44, F₂, 3, 67) (dual of [(44, 3), 10, 68]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁵⁴, 21, F₂, 3, 33) (dual of [(21, 3), 9, 34]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,29P) [i] based on function field F/F₂ with g(F) = 21 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(2⁶⁸, 23, F₂, 3, 67) (dual of [(23, 3), 1, 68]-NRT-code), using
    - strength reduction [i] based on linear OOA(2⁶⁸, 23, F₂, 3, 68) (dual of [(23, 3), 1, 69]-NRT-code), using
      - dual of repetition NRT-code with length 23 [i]
linear OOA(2¹³⁵, 45, F₂, 3, 135) (dual of [(45, 3), 0, 136]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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