MinT - Information on Result #1839382

Information on Result #1839382

OOA(2¹⁷⁷, 4325382, S₂, 5, 11), using (u,Â u+v)-construction based on

OOA(2³⁷, 131081, S₂, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(2³⁷, 262163, S₂, 5), using
  - constructionÂ X4 applied to RM(1,18) âŠ‚ K(18) [i] based on
    1. OA(2³⁶, 262144, S₂, 5), using Kerdock OA K(18) [i]
    2. linear OA(2¹⁹, 262144, F₂, 3) (dual of [262144, 262125, 4]-code or 262144-cap in PG(18,2)), using Reedâ€“Muller code RM(1,18) [i]
    3. linear OA(2¹⁸, 19, F₂, 17) (dual of [19, 1, 18]-code), using
      - strength reduction [i] based on linear OA(2¹⁸, 19, F₂, 18) (dual of [19, 1, 19]-code or 19-arc in PG(17,2)), using
        dual of repetition code with length 19 [i]
    4. linear OA(2¹, 19, F₂, 1) (dual of [19, 18, 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(2¹⁴⁰, 4194301, F₂, 5, 11) (dual of [(4194301, 5), 20971365, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁴⁰, 8388602, F₂, 3, 11) (dual of [(8388602, 3), 25165666, 12]-NRT-code), using
  - discarding factors / shortening the dual code 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(2¹⁷⁷, 4325381, S₂, 6, 11)	[i]	OOA Stacking with Additional Row
2	OOA(2¹⁷⁷, 4325381, S₂, 7, 11)	[i]
3	OOA(2¹⁷⁷, 4325381, S₂, 8, 11)	[i]
4	OOA(2¹⁷⁷, 4325381, S₂, 15, 11)	[i]