MinT - Information on Result #2996700

Information on Result #2996700

Linear OOA(2¹⁹³, 1529171, F₂, 8, 13) (dual of [(1529171, 8), 12233175, 14]-NRT-code), using 2² times duplication based on linear OOA(2¹⁹¹, 1529171, F₂, 8, 13) (dual of [(1529171, 8), 12233177, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵², 131071, F₂, 8, 6) (dual of [(131071, 8), 1048516, 7]-NRT-code), using
  - appending 2 arbitrary columns [i] based on linear OOA(2⁵², 131071, F₂, 6, 6) (dual of [(131071, 6), 786374, 7]-NRT-code), using
    - appending kth column [i] based on linear OOA(2⁵², 131071, F₂, 5, 6) (dual of [(131071, 5), 655303, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (46, 52, 131071)-net over F₂, using
        1 times m-reduction [i] based on digital (46, 53, 131071)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
2. linear OOA(2¹³⁹, 1398100, F₂, 8, 13) (dual of [(1398100, 8), 11184661, 14]-NRT-code), using
  - OOA 6-folding and stacking with additional row [i] based on linear OA(2¹³⁹, 8388601, F₂, 13) (dual of [8388601, 8388462, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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.