MinT - Information on Result #1051521

Information on Result #1051521

Linear OOA(2¹⁵⁶, 2097174, F₂, 4, 13) (dual of [(2097174, 4), 8388540, 14]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁵⁶, 4194348, F₂, 2, 13) (dual of [(4194348, 2), 8388540, 14]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹⁵⁶, 4194349, F₂, 2, 13) (dual of [(4194349, 2), 8388542, 14]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(2¹⁷, 48, F₂, 2, 6) (dual of [(48, 2), 79, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (11, 17, 48)-net over F₂, using
      - linear code embedding found in a computer search [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 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(2¹⁵⁶, 1973593, F₂, 5, 13) (dual of [(1973593, 5), 9867809, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁵⁶, 1973593, F₂, 6, 13) (dual of [(1973593, 6), 11841402, 14]-NRT-code)	[i]
3	Linear OOA(2¹⁵⁶, 1973593, F₂, 7, 13) (dual of [(1973593, 7), 13814995, 14]-NRT-code)	[i]
4	Linear OOA(2¹⁵⁶, 1973593, F₂, 8, 13) (dual of [(1973593, 8), 15788588, 14]-NRT-code)	[i]
5	Digital (143, 156, 1973593)-net over F₂	[i]