MinT - Information on Result #1539895

Information on Result #1539895

Linear OOA(4¹⁸¹, 391920, F₄, 3, 24) (dual of [(391920, 3), 1175579, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁸¹, 391920, F₄, 2, 24) (dual of [(391920, 2), 783659, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁸¹, 524293, F₄, 2, 24) (dual of [(524293, 2), 1048405, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁸¹, 1048586, F₄, 24) (dual of [1048586, 1048405, 25]-code), using
  - 1 times truncation [i] based on linear OA(4¹⁸², 1048587, F₄, 25) (dual of [1048587, 1048405, 26]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(22) [i] based on
      1. linear OA(4¹⁸¹, 1048576, F₄, 25) (dual of [1048576, 1048395, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(4¹⁷¹, 1048576, F₄, 23) (dual of [1048576, 1048405, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(4¹, 11, F₄, 1) (dual of [11, 10, 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(4¹⁸¹, 97979, F₄, 27, 24) (dual of [(97979, 27), 2645252, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row