MinT - Information on Result #1009334

Information on Result #1009334

Linear OOA(2²⁴⁶, 5592458, F₂, 3, 15) (dual of [(5592458, 3), 16777128, 16]-NRT-code), using (u,Â u+v)-construction 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(2¹⁷⁸, 2796229, F₂, 3, 15) (dual of [(2796229, 3), 8388509, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁶, 28, F₂, 3, 7) (dual of [(28, 3), 68, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (9, 16, 28)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁶², 2796201, F₂, 3, 15) (dual of [(2796201, 3), 8388441, 16]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁴⁶, 2796229, F₂, 5, 15) (dual of [(2796229, 5), 13980899, 16]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁴⁶, 2796229, F₂, 6, 15) (dual of [(2796229, 6), 16777128, 16]-NRT-code)	[i]		OOA Folding