MinT - Information on Result #945604

Information on Result #945604

Linear OOA(2¹¹⁹, 5473, F₂, 3, 16) (dual of [(5473, 3), 16300, 17]-NRT-code), using OOA 3-folding based on linear OA(2¹¹⁹, 16419, F₂, 16) (dual of [16419, 16300, 17]-code), using

1 times truncation [i] based on linear OA(2¹²⁰, 16420, F₂, 17) (dual of [16420, 16300, 18]-code), using
- constructionÂ X applied to C([0,8]) âŠ‚ C([0,6]) [i] based on
  1. linear OA(2¹¹³, 16385, F₂, 17) (dual of [16385, 16272, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
  2. linear OA(2⁸⁵, 16385, F₂, 13) (dual of [16385, 16300, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 2²⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
  3. linear OA(2⁷, 35, F₂, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), using
    - discarding factors / shortening the dual code based on linear OA(2⁷, 63, F₂, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 2⁶âˆ’1, defining interval IÂ =Â [0,1], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [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(2¹¹⁹, 4282, F₂, 4, 16) (dual of [(4282, 4), 17009, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹¹⁹, 4282, F₂, 5, 16) (dual of [(4282, 5), 21291, 17]-NRT-code)	[i]
3	Linear OOA(2¹¹⁹, 4282, F₂, 6, 16) (dual of [(4282, 6), 25573, 17]-NRT-code)	[i]
4	Linear OOA(2¹¹⁹, 4282, F₂, 7, 16) (dual of [(4282, 7), 29855, 17]-NRT-code)	[i]
5	Linear OOA(2¹¹⁹, 4282, F₂, 8, 16) (dual of [(4282, 8), 34137, 17]-NRT-code)	[i]
6	Digital (103, 119, 4282)-net over F₂	[i]