MinT - Information on Result #1165104

Information on Result #1165104

Linear OOA(2²⁴¹, 2396781, F₂, 8, 15) (dual of [(2396781, 8), 19174007, 16]-NRT-code), using OOA stacking with additional row based on linear OOA(2²⁴¹, 2396782, F₂, 7, 15) (dual of [(2396782, 7), 16777233, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁵, 2097150, F₂, 7, 7) (dual of [(2097150, 7), 14679985, 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(2¹⁷⁶, 1198391, F₂, 7, 15) (dual of [(1198391, 7), 8388561, 16]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹⁴, 20, F₂, 7, 7) (dual of [(20, 7), 126, 8]-NRT-code), using
      - appending kth column [i] based on linear OOA(2¹⁴, 20, F₂, 6, 7) (dual of [(20, 6), 106, 8]-NRT-code), using
        extracting embedded OOA [i] based on digital (7, 14, 20)-net over F₂, using
        linear code embedding found in a computer search [i]
    2. linear OOA(2¹⁶², 1198371, F₂, 7, 15) (dual of [(1198371, 7), 8388435, 16]-NRT-code), using
      - OOA 7-folding [i] based on linear OA(2¹⁶², 8388597, F₂, 15) (dual of [8388597, 8388435, 16]-code), using
        discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.