MinT - Information on Result #1080001

Information on Result #1080001

Linear OOA(2²⁵¹, 4194428, F₂, 4, 15) (dual of [(4194428, 4), 16777461, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁸, 4194302, F₂, 4, 7) (dual of [(4194302, 4), 16777140, 8]-NRT-code), using
- OOA stacking with additional row [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(2¹⁸³, 2097214, F₂, 4, 15) (dual of [(2097214, 4), 8388673, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²¹, 64, F₂, 4, 7) (dual of [(64, 4), 235, 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(2¹⁶², 2097150, F₂, 4, 15) (dual of [(2097150, 4), 8388438, 16]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2¹⁶², 8388600, F₂, 15) (dual of [8388600, 8388438, 16]-code), using
      - discarding factors / shortening the dual code 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: