MinT - Information on Result #807362

Information on Result #807362

Linear OOA(2¹⁶⁶, 1046, F₂, 2, 28) (dual of [(1046, 2), 1926, 29]-NRT-code), using OOA 2-folding based on linear OA(2¹⁶⁶, 2092, F₂, 28) (dual of [2092, 1926, 29]-code), using

1 times truncation [i] based on linear OA(2¹⁶⁷, 2093, F₂, 29) (dual of [2093, 1926, 30]-code), using
- constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [i] based on
  1. linear OA(2¹⁵⁵, 2048, F₂, 29) (dual of [2048, 1893, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
  2. linear OA(2¹²², 2048, F₂, 23) (dual of [2048, 1926, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  3. linear OA(2¹², 45, F₂, 5) (dual of [45, 33, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹², 48, F₂, 5) (dual of [48, 36, 6]-code), using
      - adding a parity check bit [i] based on linear OA(2¹¹, 47, F₂, 4) (dual of [47, 36, 5]-code), using
        extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F₂, using
        linear code embedding found in a computer search [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁶⁶, 924, F₂, 3, 28) (dual of [(924, 3), 2606, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁶⁶, 924, F₂, 4, 28) (dual of [(924, 4), 3530, 29]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁶, 924, F₂, 5, 28) (dual of [(924, 5), 4454, 29]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁶, 924, F₂, 6, 28) (dual of [(924, 6), 5378, 29]-NRT-code)	[i]
5	Linear OOA(2¹⁶⁶, 924, F₂, 7, 28) (dual of [(924, 7), 6302, 29]-NRT-code)	[i]
6	Linear OOA(2¹⁶⁶, 924, F₂, 8, 28) (dual of [(924, 8), 7226, 29]-NRT-code)	[i]
7	Digital (138, 166, 924)-net over F₂	[i]