MinT - Information on Result #816279

Information on Result #816279

Linear OOA(3²³⁹, 9852, F₃, 2, 40) (dual of [(9852, 2), 19465, 41]-NRT-code), using OOA 2-folding based on linear OA(3²³⁹, 19704, F₃, 40) (dual of [19704, 19465, 41]-code), using

discarding factors / shortening the dual code based on linear OA(3²³⁹, 19705, F₃, 40) (dual of [19705, 19466, 41]-code), using
- constructionÂ X applied to C_e(39) âŠ‚ C_e(36) [i] based on
  1. linear OA(3²³⁵, 19683, F₃, 40) (dual of [19683, 19448, 41]-code), using an extension C_e(39) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,39], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 40 [i]
  2. linear OA(3²¹⁷, 19683, F₃, 37) (dual of [19683, 19466, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [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(3²³⁹, 8302, F₃, 3, 40) (dual of [(8302, 3), 24667, 41]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²³⁹, 8302, F₃, 4, 40) (dual of [(8302, 4), 32969, 41]-NRT-code)	[i]
3	Linear OOA(3²³⁹, 8302, F₃, 5, 40) (dual of [(8302, 5), 41271, 41]-NRT-code)	[i]
4	Digital (199, 239, 8302)-net over F₃	[i]