MinT - Information on Result #1009277

Information on Result #1009277

Linear OOA(2²⁵⁰, 5592530, F₂, 3, 14) (dual of [(5592530, 3), 16777340, 15]-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(2¹⁸², 2796265, F₂, 3, 14) (dual of [(2796265, 3), 8388613, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²¹, 64, F₂, 3, 7) (dual of [(64, 3), 171, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (14, 21, 64)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁶¹, 2796201, F₂, 3, 14) (dual of [(2796201, 3), 8388442, 15]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²⁵⁰, 2796265, F₂, 5, 14) (dual of [(2796265, 5), 13981075, 15]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²⁵⁰, 2796265, F₂, 6, 14) (dual of [(2796265, 6), 16777340, 15]-NRT-code)	[i]		OOA Folding