MinT - Information on Result #2226967

Information on Result #2226967

Linear OA(2²³³, 8239, F₂, 34) (dual of [8239, 8006, 35]-code), using 1 times truncation 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, 4119, F₂, 2, 34) (dual of [(4119, 2), 8005, 35]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2²³³, 2746, F₂, 3, 34) (dual of [(2746, 3), 8005, 35]-NRT-code)	[i]
3	Linear OOA(2²³³, 2059, F₂, 4, 34) (dual of [(2059, 4), 8003, 35]-NRT-code)	[i]
4	Linear OOA(2²³³, 1647, F₂, 5, 34) (dual of [(1647, 5), 8002, 35]-NRT-code)	[i]
5	Linear OOA(2²³³, 1373, F₂, 6, 34) (dual of [(1373, 6), 8005, 35]-NRT-code)	[i]
6	Linear OOA(2²³³, 1177, F₂, 7, 34) (dual of [(1177, 7), 8006, 35]-NRT-code)	[i]
7	Linear OOA(2²³³, 1029, F₂, 8, 34) (dual of [(1029, 8), 7999, 35]-NRT-code)	[i]