MinT - Information on Result #813257

Information on Result #813257

Linear OOA(3⁹⁶, 9853, F₃, 2, 16) (dual of [(9853, 2), 19610, 17]-NRT-code), using OOA 2-folding based on linear OA(3⁹⁶, 19706, F₃, 16) (dual of [19706, 19610, 17]-code), using

1 times code embedding in larger space [i] based on linear OA(3⁹⁵, 19705, F₃, 16) (dual of [19705, 19610, 17]-code), using
- constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [i] based on
  1. linear OA(3⁹¹, 19683, F₃, 16) (dual of [19683, 19592, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
  2. linear OA(3⁷³, 19683, F₃, 13) (dual of [19683, 19610, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
  3. linear OA(3⁴, 22, F₃, 2) (dual of [22, 18, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
      - Hamming code H(4,3) [i]

Mode: Constructive and 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		Method
1	Linear OOA(3⁹⁷, 9853, F₃, 2, 16) (dual of [(9853, 2), 19609, 17]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3⁹⁶, 7974, F₃, 3, 16) (dual of [(7974, 3), 23826, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3⁹⁶, 7974, F₃, 4, 16) (dual of [(7974, 4), 31800, 17]-NRT-code)	[i]
4	Linear OOA(3⁹⁶, 7974, F₃, 5, 16) (dual of [(7974, 5), 39774, 17]-NRT-code)	[i]
5	Digital (80, 96, 7974)-net over F₃	[i]