MinT - Information on Result #1116085

Information on Result #1116085

Linear OOA(2²⁶⁰, 1677761, F₂, 5, 20) (dual of [(1677761, 5), 8388545, 21]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³⁰, 41, F₂, 5, 10) (dual of [(41, 5), 175, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁰, 20, F₂, 5, 5) (dual of [(20, 5), 90, 6]-NRT-code), using
    - appending kth column [i] based on linear OOA(2¹⁰, 20, F₂, 4, 5) (dual of [(20, 4), 70, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (5, 10, 20)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²⁰, 21, F₂, 5, 10) (dual of [(21, 5), 85, 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, 1677720, F₂, 5, 20) (dual of [(1677720, 5), 8388370, 21]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2²³⁰, 8388600, F₂, 20) (dual of [8388600, 8388370, 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		Method
1	Linear OOA(2²⁶⁰, 1677761, F₂, 6, 20) (dual of [(1677761, 6), 10066306, 21]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁶⁰, 1677761, F₂, 7, 20) (dual of [(1677761, 7), 11744067, 21]-NRT-code)	[i]
3	Linear OOA(2²⁶⁰, 1677761, F₂, 8, 20) (dual of [(1677761, 8), 13421828, 21]-NRT-code)	[i]
4	Digital (240, 260, 1677761)-net over F₂	[i]
5	Linear OOA(2²⁶⁰, 838880, F₂, 25, 20) (dual of [(838880, 25), 20971740, 21]-NRT-code)	[i]	OOA Folding and Stacking with Additional Row