MinT - Information on Result #1665383

Information on Result #1665383

Linear OOA(2¹⁶⁰, 2796328, F₂, 6, 12) (dual of [(2796328, 6), 16777808, 13]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶⁰, 2796328, F₂, 3, 12) (dual of [(2796328, 3), 8388824, 13]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁶⁰, 2796328, F₂, 3, 13) (dual of [(2796328, 3), 8388824, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2²¹, 127, F₂, 3, 6) (dual of [(127, 3), 360, 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]
  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(2¹⁶⁰, 2796327, F₂, 7, 12) (dual of [(2796327, 7), 19574129, 13]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁶⁰, 2796327, F₂, 8, 12) (dual of [(2796327, 8), 22370456, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁰, 2796327, F₂, 18, 12) (dual of [(2796327, 18), 50333726, 13]-NRT-code)	[i]