MinT - Information on Result #1025341

Information on Result #1025341

Linear OOA(2²¹⁰, 73, F₂, 3, 116) (dual of [(73, 3), 9, 117]-NRT-code), using juxtaposition based on

linear OOA(2¹⁸, 9, F₂, 3, 13) (dual of [(9, 3), 9, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,13P) [i] based on function field F/F₂ with g(F) = 5 and N(F) ≥ 9, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁸³, 64, F₂, 3, 102) (dual of [(64, 3), 9, 103]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹⁸, 9, F₂, 3, 13) (dual of [(9, 3), 9, 14]-NRT-code) (see above)
  2. linear OOA(2¹⁵⁶, 55, F₂, 3, 88) (dual of [(55, 3), 9, 89]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2¹⁵⁶, 57, F₂, 3, 88) (dual of [(57, 3), 15, 89]-NRT-code), using
      - strength reduction [i] based on linear OOA(2¹⁵⁶, 57, F₂, 3, 90) (dual of [(57, 3), 15, 91]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(8¹⁴, 19, F₈, 12) (dual of [19, 5, 13]-code), using
        1 times truncation [i] based on linear OA(8¹⁵, 20, F₈, 13) (dual of [20, 5, 14]-code), using
        generator matrices provided on Edelâ€™s homepage [i]
        linear OOA(2⁶, 3, F₂, 3, 6) (dual of [(3, 3), 3, 7]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(3;3,2) [i]

Mode: Constructive and linear.

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