MinT - Information on Result #2921624

Information on Result #2921624

Linear OOA(2²⁵³, 1398123, F₂, 6, 21) (dual of [(1398123, 6), 8388485, 22]-NRT-code), using 2¹ times duplication based on linear OOA(2²⁵², 1398123, F₂, 6, 21) (dual of [(1398123, 6), 8388486, 22]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²¹, 23, F₂, 6, 10) (dual of [(23, 6), 117, 11]-NRT-code), using
  - extracting embedded OOA [i] based on digital (11, 21, 23)-net over F₂, using
    - linear code embedding found in a computer search [i]
2. linear OOA(2²³¹, 1398100, F₂, 6, 21) (dual of [(1398100, 6), 8388369, 22]-NRT-code), using
  - OOA 6-folding [i] based on linear OA(2²³¹, 8388600, F₂, 21) (dual of [8388600, 8388369, 22]-code), using
    - discarding factors / shortening the dual code 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(2²⁵³, 1237314, F₂, 7, 21) (dual of [(1237314, 7), 8660945, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁵³, 1237314, F₂, 8, 21) (dual of [(1237314, 8), 9898259, 22]-NRT-code)	[i]
3	Digital (232, 253, 1237314)-net over F₂	[i]