MinT - Information on Result #946922

Information on Result #946922

Linear OOA(2¹⁹⁰, 2742, F₂, 3, 28) (dual of [(2742, 3), 8036, 29]-NRT-code), using OOA 3-folding based on linear OA(2¹⁹⁰, 8226, F₂, 28) (dual of [8226, 8036, 29]-code), using

2 times code embedding in larger space [i] based on linear OA(2¹⁸⁸, 8224, F₂, 28) (dual of [8224, 8036, 29]-code), using
- 1 times truncation [i] based on linear OA(2¹⁸⁹, 8225, F₂, 29) (dual of [8225, 8036, 30]-code), using
  - constructionÂ X applied to C([0,14]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(2¹⁸³, 8193, F₂, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]
    2. linear OA(2¹⁵⁷, 8193, F₂, 25) (dual of [8193, 8036, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    3. 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(2¹⁹³, 2743, F₂, 3, 28) (dual of [(2743, 3), 8036, 29]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁹¹, 2742, F₂, 3, 28) (dual of [(2742, 3), 8035, 29]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁹², 2742, F₂, 3, 28) (dual of [(2742, 3), 8034, 29]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2¹⁹⁰, 2137, F₂, 4, 28) (dual of [(2137, 4), 8358, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(2¹⁹⁰, 2137, F₂, 5, 28) (dual of [(2137, 5), 10495, 29]-NRT-code)	[i]
6	Linear OOA(2¹⁹⁰, 2137, F₂, 6, 28) (dual of [(2137, 6), 12632, 29]-NRT-code)	[i]
7	Linear OOA(2¹⁹⁰, 2137, F₂, 7, 28) (dual of [(2137, 7), 14769, 29]-NRT-code)	[i]
8	Linear OOA(2¹⁹⁰, 2137, F₂, 8, 28) (dual of [(2137, 8), 16906, 29]-NRT-code)	[i]
9	Digital (162, 190, 2137)-net over F₂	[i]