MinT - Information on Result #1235351

Information on Result #1235351

Linear OOA(2²⁶⁰, 4299157, F₂, 5, 12) (dual of [(4299157, 5), 21495525, 13]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁴, 2097150, F₂, 5, 6) (dual of [(2097150, 5), 10485686, 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(2¹⁹⁶, 2202007, F₂, 5, 12) (dual of [(2202007, 5), 11009839, 13]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁵⁸, 524287, F₂, 5, 6) (dual of [(524287, 5), 2621377, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F₂, using
      - 1 times m-reduction [i] based on digital (52, 59, 524287)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
  2. linear OOA(2¹³⁸, 1677720, F₂, 5, 12) (dual of [(1677720, 5), 8388462, 13]-NRT-code), using
    - OOA 5-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.