MinT - Information on Result #1831527

Information on Result #1831527

OOA(2¹⁹⁸, 4196356, S₂, 2, 14), using (u,Â u+v)-construction based on

OOA(2³⁷, 2055, S₂, 2, 7), using
- OOA 2-folding [i] based on OA(2³⁷, 4110, S₂, 7), using
  - 1 times code embedding in larger space [i] based on OA(2³⁶, 4109, S₂, 7), using
    - constructionÂ X4 applied to K(12) âŠ‚ DG(12,5) [i] based on
      1. OA(2³⁵, 4096, S₂, 7), using Delsarteâ€“Goethals OA DG(12,5) [i]
      2. OA(2²⁴, 4096, S₂, 5), using Kerdock OA K(12) [i]
      3. linear OA(2¹², 13, F₂, 11) (dual of [13, 1, 12]-code), using
        strength reduction [i] based on linear OA(2¹², 13, F₂, 12) (dual of [13, 1, 13]-code or 13-arc in PG(11,2)), using
        dual of repetition code with length 13 [i]
      4. linear OA(2¹, 13, F₂, 1) (dual of [13, 12, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
linear OOA(2¹⁶¹, 4194301, F₂, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹⁶¹, 8388602, F₂, 14) (dual of [8388602, 8388441, 15]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

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