MinT - Information on Result #2478284

Information on Result #2478284

Linear OOA(2²¹¹, large, F₂, 2, 13), using 2¹ times duplication based on linear OOA(2²¹⁰, large, F₂, 2, 13), using

2 times NRT-code embedding in larger space [i] 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		This result only	Method
1	Linear OOA(2²¹¹, large, F₂, 3, 13)	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²¹¹, large, F₂, 4, 13)	[i]
3	Linear OOA(2²¹¹, large, F₂, 5, 13)	[i]
4	Linear OOA(2²¹¹, large, F₂, 6, 13)	[i]
5	Linear OOA(2²¹¹, large, F₂, 7, 13)	[i]
6	Linear OOA(2²¹¹, large, F₂, 8, 13)	[i]
7	Digital (198, 211, large)-net over F₂	[i]