MinT - Information on Result #1840076

Information on Result #1840076

OOA(2¹⁶⁸, 4202500, S₂, 8, 10), using (u,Â u+v)-construction based on

OOA(2²⁹, 8199, S₂, 8, 5), using
- appending 3 arbitrary columns [i] based on OOA(2²⁹, 8199, S₂, 5, 5), using
  - OOA 2-folding and stacking with additional row [i] based on OA(2²⁹, 16399, S₂, 5), using
    - constructionÂ X4 applied to RM(1,14) âŠ‚ K(14) [i] based on
      1. OA(2²⁸, 16384, S₂, 5), using Kerdock OA K(14) [i]
      2. linear OA(2¹⁵, 16384, F₂, 3) (dual of [16384, 16369, 4]-code or 16384-cap in PG(14,2)), using Reedâ€“Muller code RM(1,14) [i]
      3. linear OA(2¹⁴, 15, F₂, 13) (dual of [15, 1, 14]-code), using
        strength reduction [i] based on linear OA(2¹⁴, 15, F₂, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
        dual of repetition code with length 15 [i]
      4. linear OA(2¹, 15, F₂, 1) (dual of [15, 14, 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(2¹³⁹, 4194301, F₂, 8, 10) (dual of [(4194301, 8), 33554269, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (129, 139, 4194301)-net over F₂, using
  - 1 times m-reduction [i] based on digital (129, 140, 4194301)-net over F₂, using
    - net defined by OOA [i] based on linear OOA(2¹⁴⁰, 4194301, F₂, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
        OOAs constructed from BCH codes [i]

Mode: Constructive.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.