MinT - Information on Result #1234983

Information on Result #1234983

Linear OOA(2²¹⁵, 4194323, F₂, 4, 12) (dual of [(4194323, 4), 16777077, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁴, 2097150, F₂, 4, 6) (dual of [(2097150, 4), 8388536, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (58, 64, 2097150)-net over F₂, using
  - 1 times m-reduction [i] based on digital (58, 65, 2097150)-net over F₂, using
    - net defined by OOA [i] based on linear OOA(2⁶⁵, 2097150, F₂, 7, 7) (dual of [(2097150, 7), 14679985, 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(2¹⁵¹, 2097173, F₂, 4, 12) (dual of [(2097173, 4), 8388541, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹³, 23, F₂, 4, 6) (dual of [(23, 4), 79, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 13, 23)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹³⁸, 2097150, F₂, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using
      - discarding factors / shortening the dual code 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.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.