MinT - Information on Result #1079795

Information on Result #1079795

Linear OOA(2²³³, 4194810, F₂, 4, 13) (dual of [(4194810, 4), 16779007, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁵, 2097150, F₂, 4, 6) (dual of [(2097150, 4), 8388535, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 6) (dual of [(2097151, 3), 6291388, 7]-NRT-code), using
  - strength reduction [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(2¹⁶⁸, 2097660, F₂, 4, 13) (dual of [(2097660, 4), 8390472, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²⁹, 510, F₂, 4, 6) (dual of [(510, 4), 2011, 7]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2²⁹, 511, F₂, 3, 6) (dual of [(511, 3), 1504, 7]-NRT-code), using
      - strength reduction [i] based on linear OOA(2²⁹, 511, F₂, 3, 7) (dual of [(511, 3), 1504, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
  2. linear OOA(2¹³⁹, 2097150, F₂, 4, 13) (dual of [(2097150, 4), 8388461, 14]-NRT-code), using
    - OOA 4-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 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.