MinT - Information on Result #1051745

Information on Result #1051745

Linear OOA(2¹⁷⁸, 2097164, F₂, 4, 15) (dual of [(2097164, 4), 8388478, 16]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁷⁸, 4194328, F₂, 2, 15) (dual of [(4194328, 2), 8388478, 16]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷⁸, 4194329, F₂, 2, 15) (dual of [(4194329, 2), 8388480, 16]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁶, 28, F₂, 2, 7) (dual of [(28, 2), 40, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (9, 16, 28)-net over F₂, using
      - linear code embedding found in a computer search [i]
  2. linear OOA(2¹⁶², 4194301, F₂, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(2¹⁶², 8388602, F₂, 15) (dual of [8388602, 8388440, 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.