MinT - Information on Result #947591

Information on Result #947591

Linear OOA(2²³³, 2746, F₂, 3, 34) (dual of [(2746, 3), 8005, 35]-NRT-code), using OOA 3-folding based on linear OA(2²³³, 8238, F₂, 34) (dual of [8238, 8005, 35]-code), using

discarding factors / shortening the dual code based on linear OA(2²³³, 8239, F₂, 34) (dual of [8239, 8006, 35]-code), using
- 1 times truncation [i] based on linear OA(2²³⁴, 8240, F₂, 35) (dual of [8240, 8006, 36]-code), using
  - constructionÂ X applied to C_e(34) âŠ‚ C_e(28) [i] based on
    1. linear OA(2²²², 8192, F₂, 35) (dual of [8192, 7970, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
    2. linear OA(2¹⁸³, 8192, F₂, 29) (dual of [8192, 8009, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(2²³³, 2404, F₂, 4, 34) (dual of [(2404, 4), 9383, 35]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³³, 2404, F₂, 5, 34) (dual of [(2404, 5), 11787, 35]-NRT-code)	[i]
3	Linear OOA(2²³³, 2404, F₂, 6, 34) (dual of [(2404, 6), 14191, 35]-NRT-code)	[i]
4	Linear OOA(2²³³, 2404, F₂, 7, 34) (dual of [(2404, 7), 16595, 35]-NRT-code)	[i]
5	Linear OOA(2²³³, 2404, F₂, 8, 34) (dual of [(2404, 8), 18999, 35]-NRT-code)	[i]
6	Digital (199, 233, 2404)-net over F₂	[i]