MinT - Information on Result #1592377

Information on Result #1592377

Linear OOA(2¹⁵⁷, 687, F₂, 4, 29) (dual of [(687, 4), 2591, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵⁷, 687, F₂, 3, 29) (dual of [(687, 3), 1904, 30]-NRT-code), using

OOA 3-folding [i] based on linear OA(2¹⁵⁷, 2061, F₂, 29) (dual of [2061, 1904, 30]-code), using
- 1 times code embedding in larger space [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: 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		This result only	Method
1	Linear OOA(2¹⁵⁸, 687, F₂, 4, 29) (dual of [(687, 4), 2590, 30]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁵⁹, 687, F₂, 4, 29) (dual of [(687, 4), 2589, 30]-NRT-code)	[i]		OOA Duplication
3	Linear OOA(2¹⁵⁷, 343, F₂, 7, 29) (dual of [(343, 7), 2244, 30]-NRT-code)	[i]		OOA Folding
4	Linear OOA(2¹⁵⁷, 343, F₂, 8, 29) (dual of [(343, 8), 2587, 30]-NRT-code)	[i]		OOA Folding