MinT - Information on Result #1150944

Information on Result #1150944

Linear OOA(2²⁴⁹, 2097213, F₂, 7, 14) (dual of [(2097213, 7), 14680242, 15]-NRT-code), using OOA 2-folding based on linear OOA(2²⁴⁹, 4194426, F₂, 4, 14) (dual of [(4194426, 4), 16777455, 15]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2²⁴⁹, 4194427, F₂, 4, 14) (dual of [(4194427, 4), 16777459, 15]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2⁶⁵, 2097150, F₂, 4, 7) (dual of [(2097150, 4), 8388535, 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]
  2. linear OOA(2¹⁸⁴, 2097277, F₂, 4, 14) (dual of [(2097277, 4), 8388924, 15]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2²³, 127, F₂, 4, 7) (dual of [(127, 4), 485, 8]-NRT-code), using
        extracting embedded OOA [i] based on digital (16, 23, 127)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
      2. linear OOA(2¹⁶¹, 2097150, F₂, 4, 14) (dual of [(2097150, 4), 8388439, 15]-NRT-code), using
        OOA 4-folding [i] based on linear OA(2¹⁶¹, 8388600, F₂, 14) (dual of [8388600, 8388439, 15]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
        the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.