MinT - Information on Result #1052034

Information on Result #1052034

Linear OOA(2²²⁵, 2097406, F₂, 4, 17) (dual of [(2097406, 4), 8389399, 18]-NRT-code), using OOA 2-folding based on linear OOA(2²²⁵, 4194812, F₂, 2, 17) (dual of [(4194812, 2), 8389399, 18]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²²⁵, 4194813, F₂, 2, 17) (dual of [(4194813, 2), 8389401, 18]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁴⁰, 512, F₂, 2, 8) (dual of [(512, 2), 984, 9]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2⁴⁰, 1024, F₂, 8) (dual of [1024, 984, 9]-code), using
      - 1 times truncation [i] based on linear OA(2⁴¹, 1025, F₂, 9) (dual of [1025, 984, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 1025Â | 2²⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
  2. linear OOA(2¹⁸⁵, 4194301, F₂, 2, 17) (dual of [(4194301, 2), 8388417, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁸⁵, 8388602, F₂, 17) (dual of [8388602, 8388417, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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(2²²⁵, 1850659, F₂, 5, 17) (dual of [(1850659, 5), 9253070, 18]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²²⁵, 1850659, F₂, 6, 17) (dual of [(1850659, 6), 11103729, 18]-NRT-code)	[i]
3	Linear OOA(2²²⁵, 1850659, F₂, 7, 17) (dual of [(1850659, 7), 12954388, 18]-NRT-code)	[i]
4	Linear OOA(2²²⁵, 1850659, F₂, 8, 17) (dual of [(1850659, 8), 14805047, 18]-NRT-code)	[i]
5	Digital (208, 225, 1850659)-net over F₂	[i]