MinT - Information on Result #2996788

Information on Result #2996788

Linear OOA(2²⁵¹, 2396996, F₂, 8, 14) (dual of [(2396996, 8), 19175717, 15]-NRT-code), using 2² times duplication based on linear OOA(2²⁴⁹, 2396996, F₂, 8, 14) (dual of [(2396996, 8), 19175719, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁵, 2097150, F₂, 8, 7) (dual of [(2097150, 8), 16777135, 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, 1198498, F₂, 8, 14) (dual of [(1198498, 8), 9587800, 15]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2²³, 127, F₂, 8, 7) (dual of [(127, 8), 993, 8]-NRT-code), using
      - appending 1 arbitrary column [i] based on linear OOA(2²³, 127, F₂, 7, 7) (dual of [(127, 7), 866, 8]-NRT-code), using
        appending kth column [i] based on linear OOA(2²³, 127, F₂, 6, 7) (dual of [(127, 6), 739, 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, 1198371, F₂, 8, 14) (dual of [(1198371, 8), 9586807, 15]-NRT-code), using
      - OA 7-folding and stacking [i] based on linear OA(2¹⁶¹, 8388597, F₂, 14) (dual of [8388597, 8388436, 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.