MinT - Information on Result #806027

Information on Result #806027

Linear OOA(2⁹⁴, 1038, F₂, 2, 16) (dual of [(1038, 2), 1982, 17]-NRT-code), using OOA 2-folding based on linear OA(2⁹⁴, 2076, F₂, 16) (dual of [2076, 1982, 17]-code), using

1 times truncation [i] 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(2⁹⁴, 747, F₂, 3, 16) (dual of [(747, 3), 2147, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2⁹⁴, 747, F₂, 4, 16) (dual of [(747, 4), 2894, 17]-NRT-code)	[i]
3	Linear OOA(2⁹⁴, 747, F₂, 5, 16) (dual of [(747, 5), 3641, 17]-NRT-code)	[i]
4	Linear OOA(2⁹⁴, 747, F₂, 6, 16) (dual of [(747, 6), 4388, 17]-NRT-code)	[i]
5	Linear OOA(2⁹⁴, 747, F₂, 7, 16) (dual of [(747, 7), 5135, 17]-NRT-code)	[i]
6	Linear OOA(2⁹⁴, 747, F₂, 8, 16) (dual of [(747, 8), 5882, 17]-NRT-code)	[i]
7	Digital (78, 94, 747)-net over F₂	[i]