MinT - Information on Result #1143862

Information on Result #1143862

Linear OOA(2²³³, 1398134, F₂, 6, 19) (dual of [(1398134, 6), 8388571, 20]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁵, 34, F₂, 6, 9) (dual of [(34, 6), 179, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁸, 17, F₂, 6, 4) (dual of [(17, 6), 94, 5]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(2⁸, 17, F₂, 4, 4) (dual of [(17, 4), 60, 5]-NRT-code), using
      - appending kth column [i] based on linear OOA(2⁸, 17, F₂, 3, 4) (dual of [(17, 3), 43, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (4, 8, 17)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(2¹⁷, 17, F₂, 6, 9) (dual of [(17, 6), 85, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (8, 17, 17)-net over F₂, using
      - a shift-net [i]
linear OOA(2²⁰⁸, 1398100, F₂, 6, 19) (dual of [(1398100, 6), 8388392, 20]-NRT-code), using
- OOA 6-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(2²³³, 1398134, F₂, 7, 19) (dual of [(1398134, 7), 9786705, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³³, 1398134, F₂, 8, 19) (dual of [(1398134, 8), 11184839, 20]-NRT-code)	[i]
3	Digital (214, 233, 1398134)-net over F₂	[i]