MinT - Information on Result #2418117

Information on Result #2418117

Linear OOA(2⁹⁵, 1038, F₂, 2, 16) (dual of [(1038, 2), 1981, 17]-NRT-code), using strength reduction based on linear OOA(2⁹⁵, 1038, F₂, 2, 17) (dual of [(1038, 2), 1981, 18]-NRT-code), using

OOA 2-folding [i] based on linear OA(2⁹⁵, 2076, F₂, 17) (dual of [2076, 1981, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2⁹⁵, 2077, F₂, 17) (dual of [2077, 1982, 18]-code), using
  - constructionÂ X applied to C([0,8]) âŠ‚ C([0,6]) [i] based on
    1. linear OA(2⁸⁹, 2049, F₂, 17) (dual of [2049, 1960, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    2. linear OA(2⁶⁷, 2049, F₂, 13) (dual of [2049, 1982, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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(2⁹⁵, 789, F₂, 3, 16) (dual of [(789, 3), 2272, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2⁹⁵, 789, F₂, 4, 16) (dual of [(789, 4), 3061, 17]-NRT-code)	[i]
3	Linear OOA(2⁹⁵, 789, F₂, 5, 16) (dual of [(789, 5), 3850, 17]-NRT-code)	[i]
4	Linear OOA(2⁹⁵, 789, F₂, 6, 16) (dual of [(789, 6), 4639, 17]-NRT-code)	[i]
5	Linear OOA(2⁹⁵, 789, F₂, 7, 16) (dual of [(789, 7), 5428, 17]-NRT-code)	[i]
6	Linear OOA(2⁹⁵, 789, F₂, 8, 16) (dual of [(789, 8), 6217, 17]-NRT-code)	[i]
7	Digital (79, 95, 789)-net over F₂	[i]