MinT - Information on Result #2478281

Information on Result #2478281

Linear OOA(2²⁰⁸, large, F₂, 2, 13), using 1 times NRT-code embedding in larger space based on linear OOA(2²⁰⁶, 8388602, F₂, 2, 13) (dual of [(8388602, 2), 16776998, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁶⁷, 4194303, F₂, 2, 6) (dual of [(4194303, 2), 8388539, 7]-NRT-code), using
  - OOAs constructed from BCH codes [i]
2. linear OOA(2¹³⁹, 4194301, F₂, 2, 13) (dual of [(4194301, 2), 8388463, 14]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹³⁹, 8388602, F₂, 13) (dual of [8388602, 8388463, 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 t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰⁹, large, F₂, 2, 13)	[i]	OOA Duplication
2	Linear OOA(2²⁰⁸, 7197694, F₂, 3, 13) (dual of [(7197694, 3), 21592874, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2²⁰⁸, 7197694, F₂, 4, 13) (dual of [(7197694, 4), 28790568, 14]-NRT-code)	[i]
4	Linear OOA(2²⁰⁸, 7197694, F₂, 5, 13) (dual of [(7197694, 5), 35988262, 14]-NRT-code)	[i]
5	Linear OOA(2²⁰⁸, 7197694, F₂, 6, 13) (dual of [(7197694, 6), 43185956, 14]-NRT-code)	[i]
6	Linear OOA(2²⁰⁸, 7197694, F₂, 7, 13) (dual of [(7197694, 7), 50383650, 14]-NRT-code)	[i]
7	Linear OOA(2²⁰⁸, 7197694, F₂, 8, 13) (dual of [(7197694, 8), 57581344, 14]-NRT-code)	[i]
8	Digital (195, 208, 7197694)-net over F₂	[i]