MinT - Information on Result #807820

Information on Result #807820

Linear OOA(2¹⁸², 1038, F₂, 2, 32) (dual of [(1038, 2), 1894, 33]-NRT-code), using OOA 2-folding based on linear OA(2¹⁸², 2076, F₂, 32) (dual of [2076, 1894, 33]-code), using

1 times truncation [i] based on linear OA(2¹⁸³, 2077, F₂, 33) (dual of [2077, 1894, 34]-code), using
- constructionÂ X applied to C([0,16]) âŠ‚ C([0,14]) [i] based on
  1. linear OA(2¹⁷⁷, 2049, F₂, 33) (dual of [2049, 1872, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
  2. linear OA(2¹⁵⁵, 2049, F₂, 29) (dual of [2049, 1894, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049Â | 2²²âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (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(2¹⁸⁶, 1040, F₂, 2, 32) (dual of [(1040, 2), 1894, 33]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁸², 821, F₂, 3, 32) (dual of [(821, 3), 2281, 33]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁸², 821, F₂, 4, 32) (dual of [(821, 4), 3102, 33]-NRT-code)	[i]
4	Linear OOA(2¹⁸², 821, F₂, 5, 32) (dual of [(821, 5), 3923, 33]-NRT-code)	[i]
5	Linear OOA(2¹⁸², 821, F₂, 6, 32) (dual of [(821, 6), 4744, 33]-NRT-code)	[i]
6	Linear OOA(2¹⁸², 821, F₂, 7, 32) (dual of [(821, 7), 5565, 33]-NRT-code)	[i]
7	Linear OOA(2¹⁸², 821, F₂, 8, 32) (dual of [(821, 8), 6386, 33]-NRT-code)	[i]
8	Digital (150, 182, 821)-net over F₂	[i]