MinT - Information on Result #1025347

Information on Result #1025347

Linear OOA(2²⁵⁵, 88, F₂, 3, 142) (dual of [(88, 3), 9, 143]-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(2²²⁸, 79, F₂, 3, 128) (dual of [(79, 3), 9, 129]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2²²⁸, 84, F₂, 3, 128) (dual of [(84, 3), 24, 129]-NRT-code), using
  - 3 step truncation [i] based on linear OOA(2²³¹, 85, F₂, 3, 131) (dual of [(85, 3), 24, 132]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(16¹¹, 17, F₁₆, 11) (dual of [17, 6, 12]-code or 17-arc in PG(10,16)), using
        extended Reedâ€“Solomon code RS_e(6,16) [i]
        the expurgated narrow-sense BCH-code C(I) with length 17Â | 16²âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
      2. linear OOA(2¹¹, 5, F₂, 3, 10) (dual of [(5, 3), 4, 11]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(3;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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