MinT - Information on Result #2668412

Information on Result #2668412

Linear OOA(2²¹⁷, 2742, F₂, 3, 32) (dual of [(2742, 3), 8009, 33]-NRT-code), using 2¹ times duplication based on linear OOA(2²¹⁶, 2742, F₂, 3, 32) (dual of [(2742, 3), 8010, 33]-NRT-code), using

OOA 3-folding [i] 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(2²¹⁷, 2217, F₂, 4, 32) (dual of [(2217, 4), 8651, 33]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹⁷, 2217, F₂, 5, 32) (dual of [(2217, 5), 10868, 33]-NRT-code)	[i]
3	Linear OOA(2²¹⁷, 2217, F₂, 6, 32) (dual of [(2217, 6), 13085, 33]-NRT-code)	[i]
4	Linear OOA(2²¹⁷, 2217, F₂, 7, 32) (dual of [(2217, 7), 15302, 33]-NRT-code)	[i]
5	Linear OOA(2²¹⁷, 2217, F₂, 8, 32) (dual of [(2217, 8), 17519, 33]-NRT-code)	[i]
6	Digital (185, 217, 2217)-net over F₂	[i]