MinT - Information on Result #2666762

Information on Result #2666762

Linear OOA(2¹⁷⁴, 2798248, F₂, 3, 13) (dual of [(2798248, 3), 8394570, 14]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁷³, 2798248, F₂, 3, 13) (dual of [(2798248, 3), 8394571, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2³⁴, 2047, F₂, 3, 6) (dual of [(2047, 3), 6107, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (28, 34, 2047)-net over F₂, using
    - 1 times m-reduction [i] based on digital (28, 35, 2047)-net over F₂, using
      - nets constructed from net-embeddable BCH codes [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(2¹⁷⁴, 2174297, F₂, 4, 13) (dual of [(2174297, 4), 8697014, 14]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁷⁴, 2174297, F₂, 5, 13) (dual of [(2174297, 5), 10871311, 14]-NRT-code)	[i]
3	Linear OOA(2¹⁷⁴, 2174297, F₂, 6, 13) (dual of [(2174297, 6), 13045608, 14]-NRT-code)	[i]
4	Linear OOA(2¹⁷⁴, 2174297, F₂, 7, 13) (dual of [(2174297, 7), 15219905, 14]-NRT-code)	[i]
5	Linear OOA(2¹⁷⁴, 2174297, F₂, 8, 13) (dual of [(2174297, 8), 17394202, 14]-NRT-code)	[i]
6	Digital (161, 174, 2174297)-net over F₂	[i]