MinT - Information on Result #1650298

Information on Result #1650298

Linear OOA(3²²⁵, 65212, F₃, 5, 29) (dual of [(65212, 5), 325835, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²⁵, 65212, F₃, 2, 29) (dual of [(65212, 2), 130199, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²⁵, 88608, F₃, 2, 29) (dual of [(88608, 2), 176991, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²²⁵, 177216, F₃, 29) (dual of [177216, 176991, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(3²²⁵, 177217, F₃, 29) (dual of [177217, 176992, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(21) [i] based on
      1. linear OA(3²¹⁰, 177147, F₃, 29) (dual of [177147, 176937, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
      2. linear OA(3¹⁵⁵, 177147, F₃, 22) (dual of [177147, 176992, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(3¹⁵, 70, F₃, 6) (dual of [70, 55, 7]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹⁵, 85, F₃, 6) (dual of [85, 70, 7]-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(3²²⁵, 21737, F₃, 35, 29) (dual of [(21737, 35), 760570, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row