MinT - Information on Result #1175580

Information on Result #1175580

Linear OOA(2²³⁵, 2798244, F₂, 8, 13) (dual of [(2798244, 8), 22385717, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2⁶⁴, 2097149, F₂, 8, 6) (dual of [(2097149, 8), 16777128, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2⁶⁴, 2097150, F₂, 3, 6) (dual of [(2097150, 3), 6291386, 7]-NRT-code), using
  - 1 step truncation [i] based on linear OOA(2⁶⁵, 2097151, F₂, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
linear OOA(2¹⁷¹, 1399122, F₂, 8, 13) (dual of [(1399122, 8), 11192805, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2³², 1022, F₂, 8, 6) (dual of [(1022, 8), 8144, 7]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(2³², 1023, F₂, 3, 6) (dual of [(1023, 3), 3037, 7]-NRT-code), using
      - strength reduction [i] based on linear OOA(2³², 1023, F₂, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
        OOAs constructed from BCH codes [i]
  2. linear OOA(2¹³⁹, 1398100, F₂, 8, 13) (dual of [(1398100, 8), 11184661, 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.

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(2²³⁵, 2798244, F₂, 8, 12) (dual of [(2798244, 8), 22385717, 13]-NRT-code)	[i]		Strength Reduction for OOAs