MinT - Information on Result #2479498

Information on Result #2479498

Linear OOA(2¹⁵⁸, 1031, F₂, 2, 28) (dual of [(1031, 2), 1904, 29]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁵⁶, 1030, F₂, 2, 28) (dual of [(1030, 2), 1904, 29]-NRT-code), using

OOA 2-folding [i] based on linear OA(2¹⁵⁶, 2060, F₂, 28) (dual of [2060, 1904, 29]-code), using
- strength reduction [i] based on linear OA(2¹⁵⁶, 2060, F₂, 29) (dual of [2060, 1904, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(26) [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(2¹⁴⁴, 2048, F₂, 27) (dual of [2048, 1904, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [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(2¹⁵⁸, 734, F₂, 3, 28) (dual of [(734, 3), 2044, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2¹⁵⁸, 734, F₂, 4, 28) (dual of [(734, 4), 2778, 29]-NRT-code)	[i]
3	Linear OOA(2¹⁵⁸, 734, F₂, 5, 28) (dual of [(734, 5), 3512, 29]-NRT-code)	[i]
4	Linear OOA(2¹⁵⁸, 734, F₂, 6, 28) (dual of [(734, 6), 4246, 29]-NRT-code)	[i]
5	Linear OOA(2¹⁵⁸, 734, F₂, 7, 28) (dual of [(734, 7), 4980, 29]-NRT-code)	[i]
6	Linear OOA(2¹⁵⁸, 734, F₂, 8, 28) (dual of [(734, 8), 5714, 29]-NRT-code)	[i]
7	Digital (130, 158, 734)-net over F₂	[i]