MinT - Information on Result #1666249

Information on Result #1666249

Linear OOA(2¹⁷⁵, 2348372, F₂, 6, 13) (dual of [(2348372, 6), 14090057, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁷⁵, 2348372, F₂, 3, 13) (dual of [(2348372, 3), 7044941, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁷⁵, 2798248, F₂, 3, 13) (dual of [(2798248, 3), 8394569, 14]-NRT-code), using
- 2² times duplication [i] based on linear OOA(2¹⁷³, 2798248, F₂, 3, 13) (dual of [(2798248, 3), 8394571, 14]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(2³⁴, 2047, F₂, 3, 6) (dual of [(2047, 3), 6107, 7]-NRT-code), using
      - extracting embedded OOA [i] based on digital (28, 34, 2047)-net over F₂, using
        1 times m-reduction [i] based on digital (28, 35, 2047)-net over F₂, using
        nets constructed from net-embeddable BCH codes [i]
    2. linear OOA(2¹³⁹, 2796201, F₂, 3, 13) (dual of [(2796201, 3), 8388464, 14]-NRT-code), using
      - OOA 3-folding [i] 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: 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(2¹⁷⁵, 2348371, F₂, 7, 13) (dual of [(2348371, 7), 16438422, 14]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁷⁵, 2348371, F₂, 8, 13) (dual of [(2348371, 8), 18786793, 14]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁵, 2348371, F₂, 18, 13) (dual of [(2348371, 18), 42270503, 14]-NRT-code)	[i]