MinT - Information on Result #1051331

Information on Result #1051331

Linear OOA(2¹²⁸, 2097168, F₂, 4, 11) (dual of [(2097168, 4), 8388544, 12]-NRT-code), using OOA 2-folding based on linear OOA(2¹²⁸, 4194336, F₂, 2, 11) (dual of [(4194336, 2), 8388544, 12]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹²⁸, 4194337, F₂, 2, 11) (dual of [(4194337, 2), 8388546, 12]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹², 36, F₂, 2, 5) (dual of [(36, 2), 60, 6]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 12, 36)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹¹⁶, 4194301, F₂, 2, 11) (dual of [(4194301, 2), 8388486, 12]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹¹⁶, 8388602, F₂, 11) (dual of [8388602, 8388486, 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.