MinT - Information on Result #1590343

Information on Result #1590343

Linear OOA(2¹¹¹, 396, F₂, 4, 22) (dual of [(396, 4), 1473, 23]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹¹¹, 396, F₂, 2, 22) (dual of [(396, 2), 681, 23]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(2¹¹¹, 517, F₂, 2, 22) (dual of [(517, 2), 923, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2¹¹¹, 1034, F₂, 22) (dual of [1034, 923, 23]-code), using
  - 1 times truncation [i] based on linear OA(2¹¹², 1035, F₂, 23) (dual of [1035, 923, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(20) [i] based on
      1. linear OA(2¹¹¹, 1024, F₂, 23) (dual of [1024, 913, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(2¹⁰¹, 1024, F₂, 21) (dual of [1024, 923, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 2¹⁰âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      3. linear OA(2¹, 11, F₂, 1) (dual of [11, 10, 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(2¹¹¹, 198, F₂, 7, 22) (dual of [(198, 7), 1275, 23]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2¹¹¹, 198, F₂, 8, 22) (dual of [(198, 8), 1473, 23]-NRT-code)	[i]		OOA Folding