MinT - Information on Result #2613751

Information on Result #2613751

Linear OOA(2¹⁶⁰, 2796328, F₂, 3, 12) (dual of [(2796328, 3), 8388824, 13]-NRT-code), using strength reduction 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: 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		Method
1	Linear OOA(2¹⁶⁰, 2796328, F₂, 4, 12) (dual of [(2796328, 4), 11185152, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁶⁰, 2796328, F₂, 5, 12) (dual of [(2796328, 5), 13981480, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁰, 2796328, F₂, 6, 12) (dual of [(2796328, 6), 16777808, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁰, 2796328, F₂, 7, 12) (dual of [(2796328, 7), 19574136, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁶⁰, 2796328, F₂, 8, 12) (dual of [(2796328, 8), 22370464, 13]-NRT-code)	[i]
6	Digital (148, 160, 2796328)-net over F₂	[i]