MinT - Information on Result #1116047

Information on Result #1116047

Linear OOA(2²³⁸, 1677772, F₂, 5, 19) (dual of [(1677772, 5), 8388622, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2³⁰, 52, F₂, 5, 9) (dual of [(52, 5), 230, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁰, 32, F₂, 5, 4) (dual of [(32, 5), 150, 5]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(2¹⁰, 32, F₂, 4, 4) (dual of [(32, 4), 118, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹⁰, 32, F₂, 3, 4) (dual of [(32, 3), 86, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (6, 10, 32)-net over F₂, using
        linear code embedding found in a computer search [i]
  2. linear OOA(2²⁰, 26, F₂, 5, 9) (dual of [(26, 5), 110, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (11, 20, 26)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2²⁰⁸, 1677720, F₂, 5, 19) (dual of [(1677720, 5), 8388392, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2²⁰⁸, 8388600, F₂, 19) (dual of [8388600, 8388392, 20]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁰⁸, large, F₂, 19) (dual of [large, large−208, 20]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²³⁸, 1408589, F₂, 6, 19) (dual of [(1408589, 6), 8451296, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³⁸, 1408589, F₂, 7, 19) (dual of [(1408589, 7), 9859885, 20]-NRT-code)	[i]
3	Linear OOA(2²³⁸, 1408589, F₂, 8, 19) (dual of [(1408589, 8), 11268474, 20]-NRT-code)	[i]
4	Digital (219, 238, 1408589)-net over F₂	[i]