MinT - Information on Result #1592323

Information on Result #1592323

Linear OOA(2¹⁵⁶, 692, F₂, 4, 28) (dual of [(692, 4), 2612, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁵⁶, 692, F₂, 2, 28) (dual of [(692, 2), 1228, 29]-NRT-code), using

discarding factors / shortening the dual code 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: 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(2¹⁵⁶, 346, F₂, 7, 28) (dual of [(346, 7), 2266, 29]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹⁵⁶, 346, F₂, 8, 28) (dual of [(346, 8), 2612, 29]-NRT-code)	[i]		OOA Folding