MinT - Information on Result #1540607

Information on Result #1540607

Linear OOA(4¹⁹¹, 120783, F₄, 3, 28) (dual of [(120783, 3), 362158, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁹¹, 120783, F₄, 2, 28) (dual of [(120783, 2), 241375, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁹¹, 131081, F₄, 2, 28) (dual of [(131081, 2), 261971, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁹¹, 262162, F₄, 28) (dual of [262162, 261971, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁹¹, 262163, F₄, 28) (dual of [262163, 261972, 29]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(25) [i] based on
      1. linear OA(4¹⁹⁰, 262144, F₄, 29) (dual of [262144, 261954, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(4¹⁷², 262144, F₄, 26) (dual of [262144, 261972, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
      3. linear OA(4¹, 19, F₄, 1) (dual of [19, 18, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 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(4¹⁹¹, 24156, F₄, 33, 28) (dual of [(24156, 33), 796957, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row