MinT - Information on Result #1009124

Information on Result #1009124

Linear OOA(2²²³, 5592530, F₂, 3, 12) (dual of [(5592530, 3), 16777367, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁷, 4194302, F₂, 3, 6) (dual of [(4194302, 3), 12582839, 7]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2⁶⁸, 4194303, F₂, 3, 7) (dual of [(4194303, 3), 12582841, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
linear OOA(2¹⁵⁶, 2796265, F₂, 3, 12) (dual of [(2796265, 3), 8388639, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁸, 64, F₂, 3, 6) (dual of [(64, 3), 174, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (12, 18, 64)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹³⁸, 2796201, F₂, 3, 12) (dual of [(2796201, 3), 8388465, 13]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²³, 2796265, F₂, 5, 12) (dual of [(2796265, 5), 13981102, 13]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²²³, 2796265, F₂, 6, 12) (dual of [(2796265, 6), 16777367, 13]-NRT-code)	[i]		OOA Folding