MinT - Information on Result #2227052

Information on Result #2227052

Linear OA(2²⁵⁰, 16431, F₂, 34) (dual of [16431, 16181, 35]-code), using 1 times truncation based on linear OA(2²⁵¹, 16432, F₂, 35) (dual of [16432, 16181, 36]-code), using

constructionÂ X applied to C_e(34) âŠ‚ C_e(28) [i] based on
1. linear OA(2²³⁹, 16384, F₂, 35) (dual of [16384, 16145, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [i]
2. linear OA(2¹⁹⁷, 16384, F₂, 29) (dual of [16384, 16187, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 16383Â = 2¹⁴âˆ’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(2²⁵⁰, 8215, F₂, 2, 34) (dual of [(8215, 2), 16180, 35]-NRT-code)	[i]	OOA Folding
2	Linear OOA(2²⁵⁰, 5477, F₂, 3, 34) (dual of [(5477, 3), 16181, 35]-NRT-code)	[i]
3	Linear OOA(2²⁵⁰, 4107, F₂, 4, 34) (dual of [(4107, 4), 16178, 35]-NRT-code)	[i]
4	Linear OOA(2²⁵⁰, 3286, F₂, 5, 34) (dual of [(3286, 5), 16180, 35]-NRT-code)	[i]
5	Linear OOA(2²⁵⁰, 2738, F₂, 6, 34) (dual of [(2738, 6), 16178, 35]-NRT-code)	[i]
6	Linear OOA(2²⁵⁰, 2347, F₂, 7, 34) (dual of [(2347, 7), 16179, 35]-NRT-code)	[i]
7	Linear OOA(2²⁵⁰, 2053, F₂, 8, 34) (dual of [(2053, 8), 16174, 35]-NRT-code)	[i]