MinT - Information on Result #1840120

Information on Result #1840120

OOA(2¹⁷², 4227076, S₂, 15, 10), using OOA stacking with additional row based on OOA(2¹⁷², 4227077, S₂, 5, 10), using

(u,Â u+v)-construction [i] based on
1. OOA(2³³, 32776, S₂, 5, 5), using
  - OOA 2-folding and stacking with additional row [i] based on OA(2³³, 65553, S₂, 5), using
    - constructionÂ X4 applied to RM(1,16) âŠ‚ K(16) [i] based on
      1. OA(2³², 65536, S₂, 5), using Kerdock OA K(16) [i]
      2. linear OA(2¹⁷, 65536, F₂, 3) (dual of [65536, 65519, 4]-code or 65536-cap in PG(16,2)), using Reedâ€“Muller code RM(1,16) [i]
      3. linear OA(2¹⁶, 17, F₂, 15) (dual of [17, 1, 16]-code), using
        strength reduction [i] based on linear OA(2¹⁶, 17, F₂, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
        dual of repetition code with length 17 [i]
      4. linear OA(2¹, 17, F₂, 1) (dual of [17, 16, 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]
2. 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]

Mode: Constructive.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	(162, 172, 4227076)-net in base 2	[i]		Net Defined by OOA