MinT - Information on Result #1650116

Information on Result #1650116

Linear OOA(3²²³, 59926, F₃, 5, 29) (dual of [(59926, 5), 299407, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3²²³, 59926, F₃, 2, 29) (dual of [(59926, 2), 119629, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3²²³, 88602, F₃, 2, 29) (dual of [(88602, 2), 176981, 30]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3²²¹, 88601, F₃, 2, 29) (dual of [(88601, 2), 176981, 30]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3²²¹, 177202, F₃, 29) (dual of [177202, 176981, 30]-code), using
    - constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [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(3¹⁶⁶, 177147, F₃, 23) (dual of [177147, 176981, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      3. linear OA(3¹¹, 55, F₃, 5) (dual of [55, 44, 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(3²²³, 19975, F₃, 35, 29) (dual of [(19975, 35), 698902, 30]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row