MinT - Information on Result #621895

Information on Result #621895

Linear OA(2¹⁵⁵, 184, F₂, 50) (dual of [184, 29, 51]-code), using constructionÂ XX applied toD₂ âŠ‚ D₁ âŠ‚ D₀ based on

linear OA(2¹¹², 127, F₂, 54) (dual of [127, 15, 55]-code), using augmented code D₂ for uÂ =Â 7 by de Boer and Brouwer [i]
linear OA(2¹⁰⁵, 127, F₂, 46) (dual of [127, 22, 47]-code), using augmented code D₁ for uÂ =Â 7 by de Boer and Brouwer [i]
linear OA(2⁹⁸, 127, F₂, 30) (dual of [127, 29, 31]-code), using augmented code D₀ for uÂ =Â 7 by de Boer and Brouwer [i]
linear OA(2⁶, 20, F₂, 3) (dual of [20, 14, 4]-code or 20-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
  - Reedâ€“Muller code RM(1,5) [i]
  - caps in base bÂ =Â 2 [i]
linear OA(2³⁰, 37, F₂, 15) (dual of [37, 7, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2³⁰, 39, F₂, 15) (dual of [39, 9, 16]-code), using
  - constructionÂ X applied to C₂ âŠ‚ C₁ [i] based on
    1. linear OA(2²⁶, 31, F₂, 15) (dual of [31, 5, 16]-code), using code C₂ for uÂ =Â 5 by de Boer and Brouwer [i]
    2. linear OA(2²¹, 31, F₂, 11) (dual of [31, 10, 12]-code), using code C₁ for uÂ =Â 5 by de Boer and Brouwer [i]
    3. 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]

Mode: Constructive and linear.

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