MinT - Information on Result #1164482

Information on Result #1164482

Linear OOA(2¹²⁵, 1677733, F₂, 8, 11) (dual of [(1677733, 8), 13421739, 12]-NRT-code), using OOA stacking with additional row based on linear OOA(2¹²⁵, 1677734, F₂, 5, 11) (dual of [(1677734, 5), 8388545, 12]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁹, 14, F₂, 5, 5) (dual of [(14, 5), 61, 6]-NRT-code), using
  - appending kth column [i] based on linear OOA(2⁹, 14, F₂, 4, 5) (dual of [(14, 4), 47, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 9, 14)-net over F₂, using
      - linear code embedding found in a computer search [i]
2. linear OOA(2¹¹⁶, 1677720, F₂, 5, 11) (dual of [(1677720, 5), 8388484, 12]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(2¹¹⁶, 8388600, F₂, 11) (dual of [8388600, 8388484, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹¹⁶, large, F₂, 11) (dual of [large, large−116, 12]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [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.