MinT - Information on Result #1159635

Information on Result #1159635

Linear OOA(2¹⁶³, 1398230, F₂, 7, 13) (dual of [(1398230, 7), 9787447, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2²⁴, 130, F₂, 7, 6) (dual of [(130, 7), 886, 7]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(2²⁴, 130, F₂, 6, 6) (dual of [(130, 6), 756, 7]-NRT-code), using
  - appending kth column [i] based on linear OOA(2²⁴, 130, F₂, 5, 6) (dual of [(130, 5), 626, 7]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(2³, 3, F₂, 5, 3) (dual of [(3, 5), 12, 4]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(5;12,2) [i]
      2. linear OOA(2²¹, 127, F₂, 5, 6) (dual of [(127, 5), 614, 7]-NRT-code), using
        extracting embedded OOA [i] based on digital (15, 21, 127)-net over F₂, using
        linear code embedding found in a computer search [i]
linear OOA(2¹³⁹, 1398100, F₂, 7, 13) (dual of [(1398100, 7), 9786561, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2¹³⁹, 8388601, F₂, 13) (dual of [8388601, 8388462, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2²²⁷, 2796460, F₂, 7, 13) (dual of [(2796460, 7), 19574993, 14]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs