MinT - Information on Result #1235118

Information on Result #1235118

Linear OOA(3¹³², 8388600, F₃, 5, 9) (dual of [(8388600, 5), 41942868, 10]-NRT-code), using extracting embedded OOA based on digital (123, 132, 8388600)-net over F₃, using

trace code for nets [i] based on digital (57, 66, 4194300)-net over F₉, using
- net defined by OOA [i] based on linear OOA(9⁶⁶, 4194300, F₉, 10, 9) (dual of [(4194300, 10), 41942934, 10]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(9⁶⁶, 8388601, F₉, 2, 9) (dual of [(8388601, 2), 16777136, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9⁶⁶, 8388602, F₉, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-code), using
      - trace code [i] based on linear OOA(81³³, 4194301, F₈₁, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81³³, 8388602, F₈₁, 9) (dual of [8388602, 8388569, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(81³³, large, F₈₁, 9) (dual of [large, large−33, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (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		Method
1	Linear OOA(3¹³³, 8388600, F₃, 5, 9) (dual of [(8388600, 5), 41942867, 10]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹³⁴, 8388600, F₃, 5, 9) (dual of [(8388600, 5), 41942866, 10]-NRT-code)	[i]
3	Linear OOA(3¹³⁵, 8388600, F₃, 5, 9) (dual of [(8388600, 5), 41942865, 10]-NRT-code)	[i]