MinT - Information on Result #894525

Information on Result #894525

Linear OOA(2²⁵⁹, 4194336, F₂, 2, 20) (dual of [(4194336, 2), 8388413, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁹, 35, F₂, 2, 10) (dual of [(35, 2), 41, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁹, 14, F₂, 2, 5) (dual of [(14, 2), 19, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 9, 14)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2²⁰, 21, F₂, 2, 10) (dual of [(21, 2), 22, 11]-NRT-code), using
    - extracting embedded OOA [i] based on digital (10, 20, 21)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2²³⁰, 4194301, F₂, 2, 20) (dual of [(4194301, 2), 8388372, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2²³⁰, 8388602, F₂, 20) (dual of [8388602, 8388372, 21]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²³⁰, large, F₂, 20) (dual of [large, large−230, 21]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁵⁹, 2097168, F₂, 4, 20) (dual of [(2097168, 4), 8388413, 21]-NRT-code)	[i]		OOA Folding