MinT - Information on Result #2422880

Information on Result #2422880

Linear OOA(2¹⁸², 4210684, F₂, 2, 12) (dual of [(4210684, 2), 8421186, 13]-NRT-code), using strength reduction based on linear OOA(2¹⁸², 4210684, F₂, 2, 13) (dual of [(4210684, 2), 8421186, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁴³, 16383, F₂, 2, 6) (dual of [(16383, 2), 32723, 7]-NRT-code), using
  - OOAs constructed from BCH codes [i]
2. linear OOA(2¹³⁹, 4194301, F₂, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹³⁹, 8388602, F₂, 13) (dual of [8388602, 8388463, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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(2¹⁸², 4210684, F₂, 3, 12) (dual of [(4210684, 3), 12631870, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸², 4210684, F₂, 4, 12) (dual of [(4210684, 4), 16842554, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁸², 4210684, F₂, 5, 12) (dual of [(4210684, 5), 21053238, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁸², 4210684, F₂, 6, 12) (dual of [(4210684, 6), 25263922, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁸², 4210684, F₂, 7, 12) (dual of [(4210684, 7), 29474606, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁸², 4210684, F₂, 8, 12) (dual of [(4210684, 8), 33685290, 13]-NRT-code)	[i]
7	Digital (170, 182, 4210684)-net over F₂	[i]