MinT - Information on Result #946693

Information on Result #946693

Linear OOA(2¹⁸¹, 2746, F₂, 3, 26) (dual of [(2746, 3), 8057, 27]-NRT-code), using OOA 3-folding based on linear OA(2¹⁸¹, 8238, F₂, 26) (dual of [8238, 8057, 27]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁸¹, 8239, F₂, 26) (dual of [8239, 8058, 27]-code), using
- 1 times truncation [i] based on linear OA(2¹⁸², 8240, F₂, 27) (dual of [8240, 8058, 28]-code), using
  - constructionÂ X applied to C_e(26) âŠ‚ C_e(20) [i] based on
    1. linear OA(2¹⁷⁰, 8192, F₂, 27) (dual of [8192, 8022, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
    2. linear OA(2¹³¹, 8192, F₂, 21) (dual of [8192, 8061, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
    3. linear OA(2¹², 48, F₂, 5) (dual of [48, 36, 6]-code), using
      - adding a parity check bit [i] based on linear OA(2¹¹, 47, F₂, 4) (dual of [47, 36, 5]-code), using
        extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F₂, using
        linear code embedding found in a computer search [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(2¹⁸¹, 2437, F₂, 4, 26) (dual of [(2437, 4), 9567, 27]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸¹, 2437, F₂, 5, 26) (dual of [(2437, 5), 12004, 27]-NRT-code)	[i]
3	Linear OOA(2¹⁸¹, 2437, F₂, 6, 26) (dual of [(2437, 6), 14441, 27]-NRT-code)	[i]
4	Linear OOA(2¹⁸¹, 2437, F₂, 7, 26) (dual of [(2437, 7), 16878, 27]-NRT-code)	[i]
5	Linear OOA(2¹⁸¹, 2437, F₂, 8, 26) (dual of [(2437, 8), 19315, 27]-NRT-code)	[i]
6	Digital (155, 181, 2437)-net over F₂	[i]