MinT - Information on Result #1080010

Information on Result #1080010

Linear OOA(2²⁵⁹, 4195322, F₂, 4, 15) (dual of [(4195322, 4), 16781029, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁵, 2097150, F₂, 4, 7) (dual of [(2097150, 4), 8388535, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
linear OOA(2¹⁹⁴, 2098172, F₂, 4, 15) (dual of [(2098172, 4), 8392494, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2³², 1022, F₂, 4, 7) (dual of [(1022, 4), 4056, 8]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2³², 1023, F₂, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
      - OOAs constructed from BCH codes [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: