MinT - Information on Result #908908

Information on Result #908908

Linear OOA(2²⁴², 123, F₂, 2, 151) (dual of [(123, 2), 4, 152]-NRT-code), using juxtaposition based on

linear OOA(2⁴, 4, F₂, 2, 3) (dual of [(4, 2), 4, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2⁴, 7, F₂, 2, 3) (dual of [(7, 2), 10, 4]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OA(2⁴, 8, F₂, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), using
    - Reedâ€“Muller code RM(1,3) [i]
    - caps in base bÂ =Â 2 [i]
linear OOA(2²³⁴, 119, F₂, 2, 147) (dual of [(119, 2), 4, 148]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2²³⁴, 120, F₂, 2, 147) (dual of [(120, 2), 6, 148]-NRT-code), using
  - strength reduction [i] based on linear OOA(2²³⁴, 120, F₂, 2, 149) (dual of [(120, 2), 6, 150]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(4³⁷, 40, F₄, 29) (dual of [40, 3, 30]-code), using
        2 times truncation [i] based on linear OA(4³⁹, 42, F₄, 31) (dual of [42, 3, 32]-code), using
        repeating each code word 2 times [i] based on linear OA(4¹⁸, 21, F₄, 15) (dual of [21, 3, 16]-code), using
        Simplex code S(3,4) [i]
      2. linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [i]

Mode: Constructive and linear.

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