MinT - Information on Result #947246

Information on Result #947246

Linear OOA(2¹⁶⁷, 686, F₂, 3, 31) (dual of [(686, 3), 1891, 32]-NRT-code), using OOA 3-folding based on linear OA(2¹⁶⁷, 2058, F₂, 31) (dual of [2058, 1891, 32]-code), using

discarding factors / shortening the dual code based on linear OA(2¹⁶⁷, 2060, F₂, 31) (dual of [2060, 1893, 32]-code), using
- constructionÂ X applied to C_e(30) âŠ‚ C_e(28) [i] based on
  1. linear OA(2¹⁶⁶, 2048, F₂, 31) (dual of [2048, 1882, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
  2. 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]
  3. linear OA(2¹, 12, F₂, 1) (dual of [12, 11, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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(2¹⁶⁷, 686, F₂, 3, 30) (dual of [(686, 3), 1891, 31]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2¹⁶⁷, 686, F₂, 4, 31) (dual of [(686, 4), 2577, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(2¹⁶⁷, 686, F₂, 5, 31) (dual of [(686, 5), 3263, 32]-NRT-code)	[i]
4	Linear OOA(2¹⁶⁷, 686, F₂, 6, 31) (dual of [(686, 6), 3949, 32]-NRT-code)	[i]
5	Linear OOA(2¹⁶⁷, 686, F₂, 7, 31) (dual of [(686, 7), 4635, 32]-NRT-code)	[i]
6	Linear OOA(2¹⁶⁷, 686, F₂, 8, 31) (dual of [(686, 8), 5321, 32]-NRT-code)	[i]
7	Digital (136, 167, 686)-net over F₂	[i]