MinT - Information on Result #1663999

Information on Result #1663999

Linear OOA(2¹³³, 686, F₂, 6, 24) (dual of [(686, 6), 3983, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹³³, 686, F₂, 3, 24) (dual of [(686, 3), 1925, 25]-NRT-code), using

OOA 3-folding [i] based on linear OA(2¹³³, 2058, F₂, 24) (dual of [2058, 1925, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹³³, 2059, F₂, 24) (dual of [2059, 1926, 25]-code), using
  - 1 times truncation [i] based on linear OA(2¹³⁴, 2060, F₂, 25) (dual of [2060, 1926, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [i] based on
      1. 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]
      2. linear OA(2¹²², 2048, F₂, 23) (dual of [2048, 1926, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2047Â = 2¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [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(2¹³⁴, 686, F₂, 6, 24) (dual of [(686, 6), 3982, 25]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(2¹³³, 342, F₂, 30, 24) (dual of [(342, 30), 10127, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row