MinT - Information on Result #1182662

Information on Result #1182662

Digital (192, 223, 1095)-net over F₂, using net defined by OOA based on linear OOA(2²²³, 1095, F₂, 31, 31) (dual of [(1095, 31), 33722, 32]-NRT-code), using

OOA 15-folding and stacking with additional row [i] based on linear OA(2²²³, 16426, F₂, 31) (dual of [16426, 16203, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2²²³, 16429, F₂, 31) (dual of [16429, 16206, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(24) [i] based on
    1. linear OA(2²¹¹, 16384, F₂, 31) (dual of [16384, 16173, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(2¹⁶⁹, 16384, F₂, 25) (dual of [16384, 16215, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (193, 223, 1095)-net over F₂	[i]	t-Expansion
2	Digital (193, 224, 1095)-net over F₂	[i]	Net Duplication
3	Digital (194, 225, 1095)-net over F₂	[i]	Net Duplication