MinT - Information on Result #815900

Information on Result #815900

Linear OOA(3²²², 9853, F₃, 2, 37) (dual of [(9853, 2), 19484, 38]-NRT-code), using OOA 2-folding based on linear OA(3²²², 19706, F₃, 37) (dual of [19706, 19484, 38]-code), using

1 times code embedding in larger space [i] based on linear OA(3²²¹, 19705, F₃, 37) (dual of [19705, 19484, 38]-code), using
- constructionÂ X applied to C_e(36) âŠ‚ C_e(33) [i] based on
  1. 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]
  2. linear OA(3¹⁹⁹, 19683, F₃, 34) (dual of [19683, 19484, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [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(3²²², 8241, F₃, 3, 37) (dual of [(8241, 3), 24501, 38]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²²², 8241, F₃, 4, 37) (dual of [(8241, 4), 32742, 38]-NRT-code)	[i]
3	Linear OOA(3²²², 8241, F₃, 5, 37) (dual of [(8241, 5), 40983, 38]-NRT-code)	[i]
4	Digital (185, 222, 8241)-net over F₃	[i]