MinT - Information on Result #1143220

Information on Result #1143220

Linear OOA(2¹⁰⁹, 2097407, F₂, 6, 9) (dual of [(2097407, 6), 12584333, 10]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁶, 257, F₂, 6, 4) (dual of [(257, 6), 1526, 5]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(2¹⁶, 257, F₂, 4, 4) (dual of [(257, 4), 1012, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(2¹⁶, 257, F₂, 3, 4) (dual of [(257, 3), 755, 5]-NRT-code), using
    - extracting embedded OOA [i] based on digital (12, 16, 257)-net over F₂, using
      - nets constructed from net-embeddable BCH codes [i]
linear OOA(2⁹³, 2097150, F₂, 6, 9) (dual of [(2097150, 6), 12582807, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(2⁹³, 8388601, F₂, 9) (dual of [8388601, 8388508, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(2⁹³, large, F₂, 9) (dual of [large, large−93, 10]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁰⁹, 2097407, F₂, 6, 8) (dual of [(2097407, 6), 12584333, 9]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2¹¹⁰, 2097407, F₂, 6, 9) (dual of [(2097407, 6), 12584332, 10]-NRT-code)	[i]		OOA Duplication