MinT - Information on Result #621745

Information on Result #621745

Linear OA(2¹³⁶, 164, F₂, 47) (dual of [164, 28, 48]-code), using constructionÂ X applied to C₁ âŠ‚ C₀ based on

linear OA(2¹⁰⁶, 127, F₂, 47) (dual of [127, 21, 48]-code), using code C₁ for uÂ =Â 7 by de Boer and Brouwer [i]
linear OA(2⁹⁹, 127, F₂, 31) (dual of [127, 28, 32]-code), using code C₀ for uÂ =Â 7 by de Boer and Brouwer [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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