MinT - Information on Result #2428646

Information on Result #2428646

Linear OOA(2²⁴⁹, 1038, F₂, 2, 44) (dual of [(1038, 2), 1827, 45]-NRT-code), using strength reduction based on linear OOA(2²⁴⁹, 1038, F₂, 2, 45) (dual of [(1038, 2), 1827, 46]-NRT-code), using

OOA 2-folding [i] based on linear OA(2²⁴⁹, 2076, F₂, 45) (dual of [2076, 1827, 46]-code), using
- discarding factors / shortening the dual code based on linear OA(2²⁴⁹, 2077, F₂, 45) (dual of [2077, 1828, 46]-code), using
  - constructionÂ X applied to C([0,22]) âŠ‚ C([0,20]) [i] based on
    1. linear OA(2²⁴³, 2049, F₂, 45) (dual of [2049, 1806, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,22], and minimum distance dÂ â‰¥ |{−22,−21,…,22}|+1Â =Â 46 (BCH-bound) [i]
    2. 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]
    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(2²⁴⁹, 992, F₂, 3, 44) (dual of [(992, 3), 2727, 45]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁴⁹, 992, F₂, 4, 44) (dual of [(992, 4), 3719, 45]-NRT-code)	[i]
3	Linear OOA(2²⁴⁹, 992, F₂, 5, 44) (dual of [(992, 5), 4711, 45]-NRT-code)	[i]
4	Linear OOA(2²⁴⁹, 992, F₂, 6, 44) (dual of [(992, 6), 5703, 45]-NRT-code)	[i]
5	Linear OOA(2²⁴⁹, 992, F₂, 7, 44) (dual of [(992, 7), 6695, 45]-NRT-code)	[i]
6	Linear OOA(2²⁴⁹, 992, F₂, 8, 44) (dual of [(992, 8), 7687, 45]-NRT-code)	[i]
7	Digital (205, 249, 992)-net over F₂	[i]