MinT - Information on Result #1131986

Information on Result #1131986

Linear OOA(2²⁵⁴, 1398113, F₂, 6, 21) (dual of [(1398113, 6), 8388424, 22]-NRT-code), using OOA 2-folding based on linear OOA(2²⁵⁴, 2796226, F₂, 3, 21) (dual of [(2796226, 3), 8388424, 22]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²³, 25, F₂, 3, 10) (dual of [(25, 3), 52, 11]-NRT-code), using
  - extracting embedded OOA [i] based on digital (13, 23, 25)-net over F₂, using
    - 2 times m-reduction [i] based on digital (13, 25, 25)-net over F₂, using
      - a shift-net [i]
2. linear OOA(2²³¹, 2796201, F₂, 3, 21) (dual of [(2796201, 3), 8388372, 22]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(2²³¹, large, F₂, 21) (dual of [large, large−231, 22]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (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(2²⁵⁴, 1300117, F₂, 7, 21) (dual of [(1300117, 7), 9100565, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵⁴, 1300117, F₂, 8, 21) (dual of [(1300117, 8), 10400682, 22]-NRT-code)	[i]
3	Digital (233, 254, 1300117)-net over F₂	[i]