MinT - Information on Result #1591698

Information on Result #1591698

Linear OOA(2¹⁴⁴, 686, F₂, 4, 26) (dual of [(686, 4), 2600, 27]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁴⁴, 686, F₂, 3, 26) (dual of [(686, 3), 1914, 27]-NRT-code), using

OOA 3-folding [i] based on linear OA(2¹⁴⁴, 2058, F₂, 26) (dual of [2058, 1914, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁴⁴, 2059, F₂, 26) (dual of [2059, 1915, 27]-code), using
  - 1 times truncation [i] based on linear OA(2¹⁴⁵, 2060, F₂, 27) (dual of [2060, 1915, 28]-code), using
    - constructionÂ X applied to C_e(26) âŠ‚ C_e(24) [i] based on
      1. 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]
      2. linear OA(2¹³³, 2048, F₂, 25) (dual of [2048, 1915, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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(2¹⁴⁵, 686, F₂, 4, 26) (dual of [(686, 4), 2599, 27]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹⁴⁴, 343, F₂, 7, 26) (dual of [(343, 7), 2257, 27]-NRT-code)	[i]		OOA Folding
3	Linear OOA(2¹⁴⁴, 343, F₂, 8, 26) (dual of [(343, 8), 2600, 27]-NRT-code)	[i]		OOA Folding