MinT - Information on Result #947379

Information on Result #947379

Linear OOA(2²¹⁶, 2742, F₂, 3, 32) (dual of [(2742, 3), 8010, 33]-NRT-code), using OOA 3-folding based on linear OA(2²¹⁶, 8226, F₂, 32) (dual of [8226, 8010, 33]-code), using

2 times code embedding in larger space [i] based on linear OA(2²¹⁴, 8224, F₂, 32) (dual of [8224, 8010, 33]-code), using
- 1 times truncation [i] based on linear OA(2²¹⁵, 8225, F₂, 33) (dual of [8225, 8010, 34]-code), using
  - constructionÂ X applied to C([0,16]) âŠ‚ C([0,14]) [i] based on
    1. linear OA(2²⁰⁹, 8193, F₂, 33) (dual of [8193, 7984, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193Â | 2²⁶âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
    2. 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]
    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(2²¹⁹, 2743, F₂, 3, 32) (dual of [(2743, 3), 8010, 33]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²¹⁷, 2742, F₂, 3, 32) (dual of [(2742, 3), 8009, 33]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²¹⁸, 2742, F₂, 3, 32) (dual of [(2742, 3), 8008, 33]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²¹⁶, 2162, F₂, 4, 32) (dual of [(2162, 4), 8432, 33]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(2²¹⁶, 2162, F₂, 5, 32) (dual of [(2162, 5), 10594, 33]-NRT-code)	[i]
6	Linear OOA(2²¹⁶, 2162, F₂, 6, 32) (dual of [(2162, 6), 12756, 33]-NRT-code)	[i]
7	Linear OOA(2²¹⁶, 2162, F₂, 7, 32) (dual of [(2162, 7), 14918, 33]-NRT-code)	[i]
8	Linear OOA(2²¹⁶, 2162, F₂, 8, 32) (dual of [(2162, 8), 17080, 33]-NRT-code)	[i]
9	Digital (184, 216, 2162)-net over F₂	[i]