MinT - Information on Result #2788534

Information on Result #2788534

Linear OOA(2¹⁸⁹, 2097404, F₂, 4, 15) (dual of [(2097404, 4), 8389427, 16]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁸⁸, 2097404, F₂, 4, 15) (dual of [(2097404, 4), 8389428, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²⁶, 254, F₂, 4, 7) (dual of [(254, 4), 990, 8]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(2²⁶, 255, F₂, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
    - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁶², 2097150, F₂, 4, 15) (dual of [(2097150, 4), 8388438, 16]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁶², 8388600, F₂, 15) (dual of [8388600, 8388438, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁶², large, F₂, 15) (dual of [large, large−162, 16]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [0,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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, 1678911, F₂, 5, 15) (dual of [(1678911, 5), 8394366, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁸⁹, 1678911, F₂, 6, 15) (dual of [(1678911, 6), 10073277, 16]-NRT-code)	[i]
3	Linear OOA(2¹⁸⁹, 1678911, F₂, 7, 15) (dual of [(1678911, 7), 11752188, 16]-NRT-code)	[i]
4	Linear OOA(2¹⁸⁹, 1678911, F₂, 8, 15) (dual of [(1678911, 8), 13431099, 16]-NRT-code)	[i]
5	Digital (174, 189, 1678911)-net over F₂	[i]