MinT - Information on Result #2419052

Information on Result #2419052

Linear OOA(2¹¹⁷, 1038, F₂, 2, 20) (dual of [(1038, 2), 1959, 21]-NRT-code), using strength reduction based on linear OOA(2¹¹⁷, 1038, F₂, 2, 21) (dual of [(1038, 2), 1959, 22]-NRT-code), using

OOA 2-folding [i] based on linear OA(2¹¹⁷, 2076, F₂, 21) (dual of [2076, 1959, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹¹⁷, 2077, F₂, 21) (dual of [2077, 1960, 22]-code), using
  - constructionÂ X applied to C([0,10]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(2¹¹¹, 2049, F₂, 21) (dual of [2049, 1938, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    2. 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]
    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(2¹¹⁷, 756, F₂, 3, 20) (dual of [(756, 3), 2151, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹¹⁷, 756, F₂, 4, 20) (dual of [(756, 4), 2907, 21]-NRT-code)	[i]
3	Linear OOA(2¹¹⁷, 756, F₂, 5, 20) (dual of [(756, 5), 3663, 21]-NRT-code)	[i]
4	Linear OOA(2¹¹⁷, 756, F₂, 6, 20) (dual of [(756, 6), 4419, 21]-NRT-code)	[i]
5	Linear OOA(2¹¹⁷, 756, F₂, 7, 20) (dual of [(756, 7), 5175, 21]-NRT-code)	[i]
6	Linear OOA(2¹¹⁷, 756, F₂, 8, 20) (dual of [(756, 8), 5931, 21]-NRT-code)	[i]
7	Digital (97, 117, 756)-net over F₂	[i]