MinT - Information on Result #808618

Information on Result #808618

Linear OOA(2²⁵³, 2072, F₂, 2, 40) (dual of [(2072, 2), 3891, 41]-NRT-code), using OOA 2-folding based on linear OA(2²⁵³, 4144, F₂, 40) (dual of [4144, 3891, 41]-code), using

strength reduction [i] based on linear OA(2²⁵³, 4144, F₂, 41) (dual of [4144, 3891, 42]-code), using
- constructionÂ X applied to C_e(40) âŠ‚ C_e(34) [i] based on
  1. linear OA(2²⁴¹, 4096, F₂, 41) (dual of [4096, 3855, 42]-code), using an extension C_e(40) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,40], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 41 [i]
  2. linear OA(2²⁰⁵, 4096, F₂, 35) (dual of [4096, 3891, 36]-code), using an extension C_e(34) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’1, defining interval IÂ =Â [1,34], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 35 [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(2²⁵⁵, 2073, F₂, 2, 40) (dual of [(2073, 2), 3891, 41]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁵⁷, 2074, F₂, 2, 40) (dual of [(2074, 2), 3891, 41]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(2²⁵⁴, 2072, F₂, 2, 40) (dual of [(2072, 2), 3890, 41]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²⁵³, 1561, F₂, 3, 40) (dual of [(1561, 3), 4430, 41]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
5	Linear OOA(2²⁵³, 1561, F₂, 4, 40) (dual of [(1561, 4), 5991, 41]-NRT-code)	[i]
6	Linear OOA(2²⁵³, 1561, F₂, 5, 40) (dual of [(1561, 5), 7552, 41]-NRT-code)	[i]
7	Linear OOA(2²⁵³, 1561, F₂, 6, 40) (dual of [(1561, 6), 9113, 41]-NRT-code)	[i]
8	Linear OOA(2²⁵³, 1561, F₂, 7, 40) (dual of [(1561, 7), 10674, 41]-NRT-code)	[i]
9	Linear OOA(2²⁵³, 1561, F₂, 8, 40) (dual of [(1561, 8), 12235, 41]-NRT-code)	[i]
10	Digital (213, 253, 1561)-net over F₂	[i]