MinT - Information on Result #1683797

Information on Result #1683797

Linear OOA(2¹⁸¹, 43693, F₂, 7, 20) (dual of [(43693, 7), 305670, 21]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁸¹, 43693, F₂, 6, 20) (dual of [(43693, 6), 261977, 21]-NRT-code), using

OOA 6-folding [i] based on linear OA(2¹⁸¹, 262158, F₂, 20) (dual of [262158, 261977, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2¹⁸¹, 262162, F₂, 20) (dual of [262162, 261981, 21]-code), using
  - 1 times truncation [i] based on linear OA(2¹⁸², 262163, F₂, 21) (dual of [262163, 261981, 22]-code), using
    - constructionÂ X applied to C_e(20) âŠ‚ C_e(18) [i] based on
      1. linear OA(2¹⁸¹, 262144, F₂, 21) (dual of [262144, 261963, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
      2. linear OA(2¹⁶³, 262144, F₂, 19) (dual of [262144, 261981, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 2¹⁸âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
      3. linear OA(2¹, 19, F₂, 1) (dual of [19, 18, 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(2¹⁸², 43693, F₂, 7, 20) (dual of [(43693, 7), 305669, 21]-NRT-code)	[i]		OOA Duplication