MinT - Information on Result #1051752

Information on Result #1051752

Linear OOA(2¹⁹¹, 2097406, F₂, 4, 15) (dual of [(2097406, 4), 8389433, 16]-NRT-code), using OOA 2-folding based on linear OOA(2¹⁹¹, 4194812, F₂, 2, 15) (dual of [(4194812, 2), 8389433, 16]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2²⁹, 511, F₂, 2, 7) (dual of [(511, 2), 993, 8]-NRT-code), using
  - OOAs constructed from BCH codes [i]
2. linear OOA(2¹⁶², 4194301, F₂, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(2¹⁶², 8388602, F₂, 15) (dual of [8388602, 8388440, 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(2¹⁹¹, 1928564, F₂, 5, 15) (dual of [(1928564, 5), 9642629, 16]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁹¹, 1928564, F₂, 6, 15) (dual of [(1928564, 6), 11571193, 16]-NRT-code)	[i]
3	Linear OOA(2¹⁹¹, 1928564, F₂, 7, 15) (dual of [(1928564, 7), 13499757, 16]-NRT-code)	[i]
4	Linear OOA(2¹⁹¹, 1928564, F₂, 8, 15) (dual of [(1928564, 8), 15428321, 16]-NRT-code)	[i]
5	Digital (176, 191, 1928564)-net over F₂	[i]