MinT - Information on Result #808023

Information on Result #808023

Linear OOA(2¹⁷⁰, 519, F₂, 2, 34) (dual of [(519, 2), 868, 35]-NRT-code), using OOA 2-folding based on linear OA(2¹⁷⁰, 1038, F₂, 34) (dual of [1038, 868, 35]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁷⁰, 1039, F₂, 34) (dual of [1039, 869, 35]-code), using
- 1 times truncation [i] based on linear OA(2¹⁷¹, 1040, F₂, 35) (dual of [1040, 869, 36]-code), using
  - constructionÂ X applied to C_e(34) âŠ‚ C_e(30) [i] based on
    1. linear OA(2¹⁶⁶, 1024, F₂, 35) (dual of [1024, 858, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    2. linear OA(2¹⁵¹, 1024, F₂, 31) (dual of [1024, 873, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    3. linear OA(2⁵, 16, F₂, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
      - Reedâ€“Muller code RM(1,4) [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(2¹⁷⁰, 488, F₂, 3, 34) (dual of [(488, 3), 1294, 35]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁷⁰, 488, F₂, 4, 34) (dual of [(488, 4), 1782, 35]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁰, 488, F₂, 5, 34) (dual of [(488, 5), 2270, 35]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁰, 488, F₂, 6, 34) (dual of [(488, 6), 2758, 35]-NRT-code)	[i]
5	Linear OOA(2¹⁷⁰, 488, F₂, 7, 34) (dual of [(488, 7), 3246, 35]-NRT-code)	[i]
6	Linear OOA(2¹⁷⁰, 488, F₂, 8, 34) (dual of [(488, 8), 3734, 35]-NRT-code)	[i]
7	Digital (136, 170, 488)-net over F₂	[i]