MinT - Information on Result #2478275

Information on Result #2478275

Linear OOA(2¹⁹⁹, 4718589, F₂, 2, 13) (dual of [(4718589, 2), 9436979, 14]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁹⁷, 4718588, F₂, 2, 13) (dual of [(4718588, 2), 9436979, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵⁸, 524287, F₂, 2, 6) (dual of [(524287, 2), 1048516, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (52, 58, 524287)-net over F₂, using
    - 1 times m-reduction [i] based on digital (52, 59, 524287)-net over F₂, using
      - nets constructed from net-embeddable 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 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(2¹⁹⁹, 3857142, F₂, 3, 13) (dual of [(3857142, 3), 11571227, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁹⁹, 3857142, F₂, 4, 13) (dual of [(3857142, 4), 15428369, 14]-NRT-code)	[i]
3	Linear OOA(2¹⁹⁹, 3857142, F₂, 5, 13) (dual of [(3857142, 5), 19285511, 14]-NRT-code)	[i]
4	Linear OOA(2¹⁹⁹, 3857142, F₂, 6, 13) (dual of [(3857142, 6), 23142653, 14]-NRT-code)	[i]
5	Linear OOA(2¹⁹⁹, 3857142, F₂, 7, 13) (dual of [(3857142, 7), 26999795, 14]-NRT-code)	[i]
6	Linear OOA(2¹⁹⁹, 3857142, F₂, 8, 13) (dual of [(3857142, 8), 30856937, 14]-NRT-code)	[i]
7	Digital (186, 199, 3857142)-net over F₂	[i]