MinT - Information on Result #808423

Information on Result #808423

Linear OOA(2²²¹, 1046, F₂, 2, 38) (dual of [(1046, 2), 1871, 39]-NRT-code), using OOA 2-folding based on linear OA(2²²¹, 2092, F₂, 38) (dual of [2092, 1871, 39]-code), using

1 times truncation [i] based on linear OA(2²²², 2093, F₂, 39) (dual of [2093, 1871, 40]-code), using
- constructionÂ X applied to C_e(38) âŠ‚ C_e(32) [i] based on
  1. 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]
  2. linear OA(2¹⁷⁷, 2048, F₂, 33) (dual of [2048, 1871, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
  3. linear OA(2¹², 45, F₂, 5) (dual of [45, 33, 6]-code), using
    - discarding factors / shortening the dual code based on 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(2²²⁵, 1048, F₂, 2, 38) (dual of [(1048, 2), 1871, 39]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²²⁷, 1049, F₂, 2, 38) (dual of [(1049, 2), 1871, 39]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2²²¹, 1014, F₂, 3, 38) (dual of [(1014, 3), 2821, 39]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(2²²¹, 1014, F₂, 4, 38) (dual of [(1014, 4), 3835, 39]-NRT-code)	[i]
5	Linear OOA(2²²¹, 1014, F₂, 5, 38) (dual of [(1014, 5), 4849, 39]-NRT-code)	[i]
6	Linear OOA(2²²¹, 1014, F₂, 6, 38) (dual of [(1014, 6), 5863, 39]-NRT-code)	[i]
7	Linear OOA(2²²¹, 1014, F₂, 7, 38) (dual of [(1014, 7), 6877, 39]-NRT-code)	[i]
8	Linear OOA(2²²¹, 1014, F₂, 8, 38) (dual of [(1014, 8), 7891, 39]-NRT-code)	[i]
9	Digital (183, 221, 1014)-net over F₂	[i]