MinT - Information on Result #2478136

Information on Result #2478136

Linear OOA(2¹⁸³, 4210685, F₂, 2, 12) (dual of [(4210685, 2), 8421187, 13]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁸¹, 4210684, F₂, 2, 12) (dual of [(4210684, 2), 8421187, 13]-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(2¹³⁸, 4194301, F₂, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹³⁸, 8388602, F₂, 12) (dual of [8388602, 8388464, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(2¹⁸³, 4210685, F₂, 3, 12) (dual of [(4210685, 3), 12631872, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸³, 4210685, F₂, 4, 12) (dual of [(4210685, 4), 16842557, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁸³, 4210685, F₂, 5, 12) (dual of [(4210685, 5), 21053242, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁸³, 4210685, F₂, 6, 12) (dual of [(4210685, 6), 25263927, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁸³, 4210685, F₂, 7, 12) (dual of [(4210685, 7), 29474612, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁸³, 4210685, F₂, 8, 12) (dual of [(4210685, 8), 33685297, 13]-NRT-code)	[i]
7	Digital (171, 183, 4210685)-net over F₂	[i]