MinT - Information on Result #2426594

Information on Result #2426594

Linear OOA(2²²⁷, 1038, F₂, 2, 40) (dual of [(1038, 2), 1849, 41]-NRT-code), using strength reduction based on linear OOA(2²²⁷, 1038, F₂, 2, 41) (dual of [(1038, 2), 1849, 42]-NRT-code), using

OOA 2-folding [i] based on linear OA(2²²⁷, 2076, F₂, 41) (dual of [2076, 1849, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(2²²⁷, 2077, F₂, 41) (dual of [2077, 1850, 42]-code), using
  - constructionÂ X applied to C([0,20]) âŠ‚ C([0,18]) [i] based on
    1. linear OA(2²²¹, 2049, F₂, 41) (dual of [2049, 1828, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,20], and minimum distance dÂ â‰¥ |{−20,−19,…,20}|+1Â =Â 42 (BCH-bound) [i]
    2. linear OA(2¹⁹⁹, 2049, F₂, 37) (dual of [2049, 1850, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
    3. linear OA(2⁶, 28, F₂, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
      - discarding factors / shortening the dual code based on linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [i]

Mode: Constructive and linear.

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		Method
1	Linear OOA(2²²⁷, 939, F₂, 3, 40) (dual of [(939, 3), 2590, 41]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²⁷, 939, F₂, 4, 40) (dual of [(939, 4), 3529, 41]-NRT-code)	[i]
3	Linear OOA(2²²⁷, 939, F₂, 5, 40) (dual of [(939, 5), 4468, 41]-NRT-code)	[i]
4	Linear OOA(2²²⁷, 939, F₂, 6, 40) (dual of [(939, 6), 5407, 41]-NRT-code)	[i]
5	Linear OOA(2²²⁷, 939, F₂, 7, 40) (dual of [(939, 7), 6346, 41]-NRT-code)	[i]
6	Linear OOA(2²²⁷, 939, F₂, 8, 40) (dual of [(939, 8), 7285, 41]-NRT-code)	[i]
7	Digital (187, 227, 939)-net over F₂	[i]