MinT - Information on Result #1650571

Information on Result #1650571

Linear OOA(3²²⁸, 145638, F₃, 5, 28) (dual of [(145638, 5), 727962, 29]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²⁸, 145638, F₃, 3, 28) (dual of [(145638, 3), 436686, 29]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²⁸, 177166, F₃, 3, 28) (dual of [(177166, 3), 531270, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3²²⁸, 531498, F₃, 28) (dual of [531498, 531270, 29]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²²⁸, 531500, F₃, 28) (dual of [531500, 531272, 29]-code), using
    - constructionÂ X applied to C_e(27) âŠ‚ C_e(21) [i] based on
      1. linear OA(3²¹⁷, 531441, F₃, 28) (dual of [531441, 531224, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
      2. linear OA(3¹⁶⁹, 531441, F₃, 22) (dual of [531441, 531272, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [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(3²²⁸, 48545, F₃, 35, 28) (dual of [(48545, 35), 1698847, 29]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row