MinT - Information on Result #2478138

Information on Result #2478138

Linear OOA(2¹⁸⁹, 4259837, F₂, 2, 12) (dual of [(4259837, 2), 8519485, 13]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁸⁷, 4259836, F₂, 2, 12) (dual of [(4259836, 2), 8519485, 13]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁴⁹, 65535, F₂, 2, 6) (dual of [(65535, 2), 131021, 7]-NRT-code), using
  - OOAs constructed from 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(2¹⁸⁹, 4259837, F₂, 3, 12) (dual of [(4259837, 3), 12779322, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸⁹, 4259837, F₂, 4, 12) (dual of [(4259837, 4), 17039159, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁸⁹, 4259837, F₂, 5, 12) (dual of [(4259837, 5), 21298996, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁸⁹, 4259837, F₂, 6, 12) (dual of [(4259837, 6), 25558833, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁸⁹, 4259837, F₂, 7, 12) (dual of [(4259837, 7), 29818670, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁸⁹, 4259837, F₂, 8, 12) (dual of [(4259837, 8), 34078507, 13]-NRT-code)	[i]
7	Digital (177, 189, 4259837)-net over F₂	[i]