MinT - Information on Result #1839378

Information on Result #1839378

OOA(2¹⁸⁰, 4718599, S₂, 5, 10), using (u,Â u+v)-construction based on

OOA(2⁴¹, 524298, S₂, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(2⁴¹, 1048597, S₂, 5), using
  - constructionÂ X4 applied to RM(1,20) âŠ‚ K(20) [i] based on
    1. OA(2⁴⁰, 1048576, S₂, 5), using Kerdock OA K(20) [i]
    2. linear OA(2²¹, 1048576, F₂, 3) (dual of [1048576, 1048555, 4]-code or 1048576-cap in PG(20,2)), using Reedâ€“Muller code RM(1,20) [i]
    3. linear OA(2²⁰, 21, F₂, 19) (dual of [21, 1, 20]-code), using
      - strength reduction [i] based on linear OA(2²⁰, 21, F₂, 20) (dual of [21, 1, 21]-code or 21-arc in PG(19,2)), using
        dual of repetition code with length 21 [i]
    4. linear OA(2¹, 21, F₂, 1) (dual of [21, 20, 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, 5, 10) (dual of [(4194301, 5), 20971366, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹³⁹, 8388602, F₂, 3, 10) (dual of [(8388602, 3), 25165667, 11]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2¹⁴⁰, large, F₂, 3, 11), using
    - OOAs constructed from BCH codes [i]

None.

The following results depend on this result:

	Result		Method
1	OOA(2¹⁸⁰, 4718598, S₂, 6, 10)	[i]	OOA Stacking with Additional Row
2	OOA(2¹⁸⁰, 4718598, S₂, 7, 10)	[i]
3	OOA(2¹⁸⁰, 4718598, S₂, 8, 10)	[i]
4	OOA(2¹⁸⁰, 4718598, S₂, 15, 10)	[i]