MinT - Information on Result #816152

Information on Result #816152

Linear OOA(3²³⁷, 9852, F₃, 2, 39) (dual of [(9852, 2), 19467, 40]-NRT-code), using OOA 2-folding based on linear OA(3²³⁷, 19704, F₃, 39) (dual of [19704, 19467, 40]-code), using

1 times code embedding in larger space [i] based on linear OA(3²³⁶, 19703, F₃, 39) (dual of [19703, 19467, 40]-code), using
- constructionÂ X applied to C([0,19]) âŠ‚ C([0,18]) [i] based on
  1. linear OA(3²³⁵, 19684, F₃, 39) (dual of [19684, 19449, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,19], and minimum distance dÂ â‰¥ |{−19,−18,…,19}|+1Â =Â 40 (BCH-bound) [i]
  2. linear OA(3²¹⁷, 19684, F₃, 37) (dual of [19684, 19467, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,18], and minimum distance dÂ â‰¥ |{−18,−17,…,18}|+1Â =Â 38 (BCH-bound) [i]
  3. linear OA(3¹, 19, F₃, 1) (dual of [19, 18, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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, 9853, F₃, 2, 39) (dual of [(9853, 2), 19467, 40]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3²³⁸, 9852, F₃, 2, 39) (dual of [(9852, 2), 19466, 40]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²³⁷, 9260, F₃, 3, 39) (dual of [(9260, 3), 27543, 40]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3²³⁷, 9260, F₃, 4, 39) (dual of [(9260, 4), 36803, 40]-NRT-code)	[i]
5	Linear OOA(3²³⁷, 9260, F₃, 5, 39) (dual of [(9260, 5), 46063, 40]-NRT-code)	[i]
6	Digital (198, 237, 9260)-net over F₃	[i]