MinT - Information on Result #2987630

Information on Result #2987630

Linear OOA(2¹⁹⁷, 1922387, F₂, 8, 12) (dual of [(1922387, 8), 15378899, 13]-NRT-code), using strength reduction based on linear OOA(2¹⁹⁷, 1922387, F₂, 8, 13) (dual of [(1922387, 8), 15378899, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵⁸, 524287, F₂, 8, 6) (dual of [(524287, 8), 4194238, 7]-NRT-code), using
  - appending 2 arbitrary columns [i] based on linear OOA(2⁵⁸, 524287, F₂, 6, 6) (dual of [(524287, 6), 3145664, 7]-NRT-code), using
    - appending kth column [i] based on 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(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.