MinT - Information on Result #1116005

Information on Result #1116005

Linear OOA(2²³³, 1677757, F₂, 5, 18) (dual of [(1677757, 5), 8388552, 19]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁶, 37, F₂, 5, 9) (dual of [(37, 5), 159, 10]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁸, 17, F₂, 5, 4) (dual of [(17, 5), 77, 5]-NRT-code), using
    - appending 1 arbitrary column [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(2¹⁸, 20, F₂, 5, 9) (dual of [(20, 5), 82, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (9, 18, 20)-net over F₂, using
      - linear code embedding found in a computer search [i]
linear OOA(2²⁰⁷, 1677720, F₂, 5, 18) (dual of [(1677720, 5), 8388393, 19]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2²⁰⁷, 8388600, F₂, 18) (dual of [8388600, 8388393, 19]-code), using
  - discarding factors / shortening the dual code based on linear OA(2²⁰⁷, large, F₂, 18) (dual of [large, large−207, 19]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(2²³³, 1677757, F₂, 6, 18) (dual of [(1677757, 6), 10066309, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²³³, 1677757, F₂, 7, 18) (dual of [(1677757, 7), 11744066, 19]-NRT-code)	[i]
3	Linear OOA(2²³³, 1677757, F₂, 8, 18) (dual of [(1677757, 8), 13421823, 19]-NRT-code)	[i]
4	Digital (215, 233, 1677757)-net over F₂	[i]