MinT - Information on Result #808034

Information on Result #808034

Linear OOA(2¹⁹⁴, 1038, F₂, 2, 34) (dual of [(1038, 2), 1882, 35]-NRT-code), using OOA 2-folding based on linear OA(2¹⁹⁴, 2076, F₂, 34) (dual of [2076, 1882, 35]-code), using

strength reduction [i] based on linear OA(2¹⁹⁴, 2076, F₂, 35) (dual of [2076, 1882, 36]-code), using
- constructionÂ X applied to C_e(34) âŠ‚ C_e(30) [i] based on
  1. linear OA(2¹⁸⁸, 2048, F₂, 35) (dual of [2048, 1860, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
  2. linear OA(2¹⁶⁶, 2048, F₂, 31) (dual of [2048, 1882, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [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(2¹⁹⁶, 1039, F₂, 2, 34) (dual of [(1039, 2), 1882, 35]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁹⁵, 1038, F₂, 2, 34) (dual of [(1038, 2), 1881, 35]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁹⁴, 865, F₂, 3, 34) (dual of [(865, 3), 2401, 35]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹⁹⁴, 865, F₂, 4, 34) (dual of [(865, 4), 3266, 35]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁴, 865, F₂, 5, 34) (dual of [(865, 5), 4131, 35]-NRT-code)	[i]
6	Linear OOA(2¹⁹⁴, 865, F₂, 6, 34) (dual of [(865, 6), 4996, 35]-NRT-code)	[i]
7	Linear OOA(2¹⁹⁴, 865, F₂, 7, 34) (dual of [(865, 7), 5861, 35]-NRT-code)	[i]
8	Linear OOA(2¹⁹⁴, 865, F₂, 8, 34) (dual of [(865, 8), 6726, 35]-NRT-code)	[i]
9	Digital (160, 194, 865)-net over F₂	[i]