MinT - Information on Result #1053575

Information on Result #1053575

Linear OOA(2²²², 4107, F₂, 4, 30) (dual of [(4107, 4), 16206, 31]-NRT-code), using OOA 4-folding based on linear OA(2²²², 16428, F₂, 30) (dual of [16428, 16206, 31]-code), using

discarding factors / shortening the dual code based on linear OA(2²²², 16431, F₂, 30) (dual of [16431, 16209, 31]-code), using
- 1 times truncation [i] based on linear OA(2²²³, 16432, F₂, 31) (dual of [16432, 16209, 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, 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(2²²², 4107, F₂, 5, 30) (dual of [(4107, 5), 20313, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²², 4107, F₂, 6, 30) (dual of [(4107, 6), 24420, 31]-NRT-code)	[i]
3	Linear OOA(2²²², 4107, F₂, 7, 30) (dual of [(4107, 7), 28527, 31]-NRT-code)	[i]
4	Linear OOA(2²²², 4107, F₂, 8, 30) (dual of [(4107, 8), 32634, 31]-NRT-code)	[i]
5	Digital (192, 222, 4107)-net over F₂	[i]