MinT - Information on Result #1826355

Information on Result #1826355

OOA(2³⁵, 2054, S₂, 2, 6), using OOA 2-folding based on OA(2³⁵, 4108, S₂, 6), using

1 times truncation [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]

Mode: Constructive.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	OOA(2¹⁷³, 4196355, S₂, 2, 12)	[i]		(u,Â u+v)-Construction for OOAs
2	OOA(2¹⁷⁴, 4196355, S₂, 2, 13)	[i]		(u,Â u+v)-Construction for OOAs