MinT - Information on Result #2478139

Information on Result #2478139

Linear OOA(2¹⁹², 4325373, F₂, 2, 12) (dual of [(4325373, 2), 8650554, 13]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁹⁰, 4325372, F₂, 2, 12) (dual of [(4325372, 2), 8650554, 13]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁵², 131071, F₂, 2, 6) (dual of [(131071, 2), 262090, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (46, 52, 131071)-net over F₂, using
    - 1 times m-reduction [i] based on digital (46, 53, 131071)-net over F₂, using
      - nets constructed from net-embeddable BCH codes [i]
2. linear OOA(2¹³⁸, 4194301, F₂, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹³⁸, 8388602, F₂, 12) (dual of [8388602, 8388464, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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(2¹⁹², 4325373, F₂, 3, 12) (dual of [(4325373, 3), 12975927, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁹², 4325373, F₂, 4, 12) (dual of [(4325373, 4), 17301300, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁹², 4325373, F₂, 5, 12) (dual of [(4325373, 5), 21626673, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁹², 4325373, F₂, 6, 12) (dual of [(4325373, 6), 25952046, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁹², 4325373, F₂, 7, 12) (dual of [(4325373, 7), 30277419, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁹², 4325373, F₂, 8, 12) (dual of [(4325373, 8), 34602792, 13]-NRT-code)	[i]
7	Digital (180, 192, 4325373)-net over F₂	[i]