MinT - Information on Result #1051627

Information on Result #1051627

Linear OOA(2¹⁷², 2097156, F₂, 4, 14) (dual of [(2097156, 4), 8388452, 15]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁷², 4194312, F₂, 2, 14) (dual of [(4194312, 2), 8388452, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2¹¹, 11, F₂, 2, 7) (dual of [(11, 2), 11, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (4, 11, 11)-net over F₂, using
    - a shift-net [i]
2. linear OOA(2¹⁶¹, 4194301, F₂, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹⁶¹, 8388602, F₂, 14) (dual of [8388602, 8388441, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁷², 1725738, F₂, 5, 14) (dual of [(1725738, 5), 8628518, 15]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁷², 1725738, F₂, 6, 14) (dual of [(1725738, 6), 10354256, 15]-NRT-code)	[i]
3	Linear OOA(2¹⁷², 1725738, F₂, 7, 14) (dual of [(1725738, 7), 12079994, 15]-NRT-code)	[i]
4	Linear OOA(2¹⁷², 1725738, F₂, 8, 14) (dual of [(1725738, 8), 13805732, 15]-NRT-code)	[i]
5	Digital (158, 172, 1725738)-net over F₂	[i]