MinT - Information on Result #2480085

Information on Result #2480085

Linear OOA(2²²¹, 2074, F₂, 2, 35) (dual of [(2074, 2), 3927, 36]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(2²¹⁷, 2072, F₂, 2, 35) (dual of [(2072, 2), 3927, 36]-NRT-code), using

OOA 2-folding [i] based on linear OA(2²¹⁷, 4144, F₂, 35) (dual of [4144, 3927, 36]-code), using
- constructionÂ X applied to C_e(34) âŠ‚ C_e(28) [i] based on
  1. 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]
  2. linear OA(2¹⁶⁹, 4096, F₂, 29) (dual of [4096, 3927, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 4095Â = 2¹²âˆ’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(2²²¹, 1423, F₂, 3, 35) (dual of [(1423, 3), 4048, 36]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²¹, 1423, F₂, 4, 35) (dual of [(1423, 4), 5471, 36]-NRT-code)	[i]
3	Linear OOA(2²²¹, 1423, F₂, 5, 35) (dual of [(1423, 5), 6894, 36]-NRT-code)	[i]
4	Linear OOA(2²²¹, 1423, F₂, 6, 35) (dual of [(1423, 6), 8317, 36]-NRT-code)	[i]
5	Linear OOA(2²²¹, 1423, F₂, 7, 35) (dual of [(1423, 7), 9740, 36]-NRT-code)	[i]
6	Linear OOA(2²²¹, 1423, F₂, 8, 35) (dual of [(1423, 8), 11163, 36]-NRT-code)	[i]
7	Digital (186, 221, 1423)-net over F₂	[i]