MinT - Information on Result #1645637

Information on Result #1645637

Linear OOA(3¹⁶⁶, 83969, F₃, 5, 21) (dual of [(83969, 5), 419679, 22]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(3¹⁶⁶, 83969, F₃, 2, 21) (dual of [(83969, 2), 167772, 22]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(3¹⁶⁶, 88601, F₃, 2, 21) (dual of [(88601, 2), 177036, 22]-NRT-code), using
- strength reduction [i] based on linear OOA(3¹⁶⁶, 88601, F₃, 2, 22) (dual of [(88601, 2), 177036, 23]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(3¹⁶⁶, 177202, F₃, 22) (dual of [177202, 177036, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [i] based on
      1. 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]
      2. linear OA(3¹¹¹, 177147, F₃, 16) (dual of [177147, 177036, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(3¹⁶⁶, 41984, F₃, 25, 21) (dual of [(41984, 25), 1049434, 22]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row