MinT - Information on Result #1175809

Information on Result #1175809

Linear OOA(2²¹⁴, 1048635, F₂, 8, 17) (dual of [(1048635, 8), 8388866, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁹, 60, F₂, 8, 8) (dual of [(60, 8), 451, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(2²⁹, 60, F₂, 7, 8) (dual of [(60, 7), 391, 9]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2¹⁰, 32, F₂, 7, 4) (dual of [(32, 7), 214, 5]-NRT-code), using
      - appending 3 arbitrary columns [i] based on linear OOA(2¹⁰, 32, F₂, 4, 4) (dual of [(32, 4), 118, 5]-NRT-code), using
        appending kth column [i] based on linear OOA(2¹⁰, 32, F₂, 3, 4) (dual of [(32, 3), 86, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (6, 10, 32)-net over F₂, using
        linear code embedding found in a computer search [i]
    2. linear OOA(2¹⁹, 30, F₂, 7, 8) (dual of [(30, 7), 191, 9]-NRT-code), using
      - extracting embedded OOA [i] based on digital (11, 19, 30)-net over F₂, using
        linear code embedding found in a computer search [i]
linear OOA(2¹⁸⁵, 1048575, F₂, 8, 17) (dual of [(1048575, 8), 8388415, 18]-NRT-code), using
- OOA 8-folding [i] based on linear OA(2¹⁸⁵, 8388600, F₂, 17) (dual of [8388600, 8388415, 18]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²¹⁴, 1048634, F₂, 24, 17) (dual of [(1048634, 24), 25167002, 18]-NRT-code)	[i]		OOA Stacking with Additional Row