MinT - Information on Result #1651692

Information on Result #1651692

Linear OOA(3²⁴⁰, 169685, F₃, 5, 29) (dual of [(169685, 5), 848185, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²⁴⁰, 169685, F₃, 3, 29) (dual of [(169685, 3), 508815, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²⁴⁰, 177166, F₃, 3, 29) (dual of [(177166, 3), 531258, 30]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²⁴⁰, 531498, F₃, 29) (dual of [531498, 531258, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²⁴⁰, 531500, F₃, 29) (dual of [531500, 531260, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [i] based on
      1. linear OA(3²²⁹, 531441, F₃, 29) (dual of [531441, 531212, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(3¹⁸¹, 531441, F₃, 23) (dual of [531441, 531260, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(3¹¹, 59, F₃, 5) (dual of [59, 48, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3²⁴⁰, 56561, F₃, 35, 29) (dual of [(56561, 35), 1979395, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row