MinT - Information on Result #908561

Information on Result #908561

Linear OOA(2¹⁷², 90, F₂, 2, 88) (dual of [(90, 2), 8, 89]-NRT-code), using juxtaposition based on

linear OOA(2¹², 10, F₂, 2, 8) (dual of [(10, 2), 8, 9]-NRT-code), using
- an explicit generator matrix by Edel [i]
linear OOA(2¹⁵², 80, F₂, 2, 79) (dual of [(80, 2), 8, 80]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2¹⁵², 84, F₂, 2, 79) (dual of [(84, 2), 16, 80]-NRT-code), using
  - 2 step truncation [i] based on linear OOA(2¹⁵⁴, 85, F₂, 2, 81) (dual of [(85, 2), 16, 82]-NRT-code), using
    - strength reduction [i] based on linear OOA(2¹⁵⁴, 85, F₂, 2, 83) (dual of [(85, 2), 16, 84]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(16¹³, 17, F₁₆, 13) (dual of [17, 4, 14]-code or 17-arc in PG(12,16)), using
        extended Reedâ€“Solomon code RS_e(4,16) [i]
        the expurgated narrow-sense BCH-code C(I) with length 17Â | 16²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
        linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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