MinT - Information on Result #808607

Information on Result #808607

Linear OOA(2²²¹, 1029, F₂, 2, 40) (dual of [(1029, 2), 1837, 41]-NRT-code), using OOA 2-folding based on linear OA(2²²¹, 2058, F₂, 40) (dual of [2058, 1837, 41]-code), using

discarding factors / shortening the dual code based on linear OA(2²²¹, 2059, F₂, 40) (dual of [2059, 1838, 41]-code), using
- 1 times truncation [i] based on linear OA(2²²², 2060, F₂, 41) (dual of [2060, 1838, 42]-code), using
  - constructionÂ X applied to C_e(40) âŠ‚ C_e(38) [i] based on
    1. linear OA(2²²¹, 2048, F₂, 41) (dual of [2048, 1827, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
    2. linear OA(2²¹⁰, 2048, F₂, 39) (dual of [2048, 1838, 40]-code), using an extension C_e(38) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,38], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 39 [i]
    3. linear OA(2¹, 12, F₂, 1) (dual of [12, 11, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(2²²¹, 834, F₂, 3, 40) (dual of [(834, 3), 2281, 41]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²¹, 834, F₂, 4, 40) (dual of [(834, 4), 3115, 41]-NRT-code)	[i]
3	Linear OOA(2²²¹, 834, F₂, 5, 40) (dual of [(834, 5), 3949, 41]-NRT-code)	[i]
4	Linear OOA(2²²¹, 834, F₂, 6, 40) (dual of [(834, 6), 4783, 41]-NRT-code)	[i]
5	Linear OOA(2²²¹, 834, F₂, 7, 40) (dual of [(834, 7), 5617, 41]-NRT-code)	[i]
6	Linear OOA(2²²¹, 834, F₂, 8, 40) (dual of [(834, 8), 6451, 41]-NRT-code)	[i]
7	Digital (181, 221, 834)-net over F₂	[i]