MinT - Information on Result #1009115

Information on Result #1009115

Linear OOA(2²¹⁴, 5592420, F₂, 3, 12) (dual of [(5592420, 3), 16777046, 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(2¹⁴⁷, 2796210, F₂, 3, 12) (dual of [(2796210, 3), 8388483, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁹, 9, F₂, 3, 6) (dual of [(9, 3), 18, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (3, 9, 9)-net over F₂, using
      - a shift-net [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(2²¹⁴, 2796210, F₂, 5, 12) (dual of [(2796210, 5), 13980836, 13]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²¹⁴, 2796210, F₂, 6, 12) (dual of [(2796210, 6), 16777046, 13]-NRT-code)	[i]		OOA Folding