MinT - Information on Result #1132646

Information on Result #1132646

Linear OOA(2²⁵⁰, 21853, F₂, 6, 28) (dual of [(21853, 6), 130868, 29]-NRT-code), using OOA 6-folding based on linear OA(2²⁵⁰, 131118, F₂, 28) (dual of [131118, 130868, 29]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁵⁰, 131119, F₂, 28) (dual of [131119, 130869, 29]-code), using
- 1 times truncation [i] based on linear OA(2²⁵¹, 131120, F₂, 29) (dual of [131120, 130869, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [i] based on
    1. linear OA(2²³⁹, 131072, F₂, 29) (dual of [131072, 130833, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
    2. linear OA(2¹⁸⁸, 131072, F₂, 23) (dual of [131072, 130884, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 131071Â = 2¹⁷âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(2²⁵⁰, 21853, F₂, 7, 28) (dual of [(21853, 7), 152721, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵⁰, 21853, F₂, 8, 28) (dual of [(21853, 8), 174574, 29]-NRT-code)	[i]
3	Digital (222, 250, 21853)-net over F₂	[i]