MinT - Information on Result #808617

Information on Result #808617

Linear OOA(2²⁵², 2071, F₂, 2, 40) (dual of [(2071, 2), 3890, 41]-NRT-code), using OOA 2-folding based on linear OA(2²⁵², 4142, F₂, 40) (dual of [4142, 3890, 41]-code), using

discarding factors / shortening the dual code based on linear OA(2²⁵², 4143, F₂, 40) (dual of [4143, 3891, 41]-code), using
- 1 times truncation [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(2²⁵², 1531, F₂, 3, 40) (dual of [(1531, 3), 4341, 41]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵², 1531, F₂, 4, 40) (dual of [(1531, 4), 5872, 41]-NRT-code)	[i]
3	Linear OOA(2²⁵², 1531, F₂, 5, 40) (dual of [(1531, 5), 7403, 41]-NRT-code)	[i]
4	Linear OOA(2²⁵², 1531, F₂, 6, 40) (dual of [(1531, 6), 8934, 41]-NRT-code)	[i]
5	Linear OOA(2²⁵², 1531, F₂, 7, 40) (dual of [(1531, 7), 10465, 41]-NRT-code)	[i]
6	Linear OOA(2²⁵², 1531, F₂, 8, 40) (dual of [(1531, 8), 11996, 41]-NRT-code)	[i]
7	Digital (212, 252, 1531)-net over F₂	[i]