MinT - Information on Result #1175808

Information on Result #1175808

Linear OOA(2²¹³, 1048628, F₂, 8, 17) (dual of [(1048628, 8), 8388811, 18]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁸, 53, F₂, 8, 8) (dual of [(53, 8), 396, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(2²⁸, 53, F₂, 7, 8) (dual of [(53, 7), 343, 9]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2⁹, 23, F₂, 7, 4) (dual of [(23, 7), 152, 5]-NRT-code), using
      - appending 3 arbitrary columns [i] based on linear OOA(2⁹, 23, F₂, 4, 4) (dual of [(23, 4), 83, 5]-NRT-code), using
        appending kth column [i] based on linear OOA(2⁹, 23, F₂, 3, 4) (dual of [(23, 3), 60, 5]-NRT-code), using
        extracting embedded OOA [i] based on digital (5, 9, 23)-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(2²¹³, 1048627, F₂, 24, 17) (dual of [(1048627, 24), 25166835, 18]-NRT-code)	[i]		OOA Stacking with Additional Row