MinT - Information on Result #807127

Information on Result #807127

Linear OOA(2¹⁵⁰, 1038, F₂, 2, 26) (dual of [(1038, 2), 1926, 27]-NRT-code), using OOA 2-folding based on linear OA(2¹⁵⁰, 2076, F₂, 26) (dual of [2076, 1926, 27]-code), using

strength reduction [i] based on linear OA(2¹⁵⁰, 2076, F₂, 27) (dual of [2076, 1926, 28]-code), using
- constructionÂ X applied to C_e(26) âŠ‚ C_e(22) [i] based on
  1. linear OA(2¹⁴⁴, 2048, F₂, 27) (dual of [2048, 1904, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
  2. linear OA(2¹²², 2048, F₂, 23) (dual of [2048, 1926, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(2¹⁵², 1039, F₂, 2, 26) (dual of [(1039, 2), 1926, 27]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁵¹, 1038, F₂, 2, 26) (dual of [(1038, 2), 1925, 27]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁵⁰, 783, F₂, 3, 26) (dual of [(783, 3), 2199, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2¹⁵⁰, 783, F₂, 4, 26) (dual of [(783, 4), 2982, 27]-NRT-code)	[i]
5	Linear OOA(2¹⁵⁰, 783, F₂, 5, 26) (dual of [(783, 5), 3765, 27]-NRT-code)	[i]
6	Linear OOA(2¹⁵⁰, 783, F₂, 6, 26) (dual of [(783, 6), 4548, 27]-NRT-code)	[i]
7	Linear OOA(2¹⁵⁰, 783, F₂, 7, 26) (dual of [(783, 7), 5331, 27]-NRT-code)	[i]
8	Linear OOA(2¹⁵⁰, 783, F₂, 8, 26) (dual of [(783, 8), 6114, 27]-NRT-code)	[i]
9	Digital (124, 150, 783)-net over F₂	[i]