MinT - Information on Result #2488247

Information on Result #2488247

Linear OOA(3²³⁹, 9853, F₃, 2, 39) (dual of [(9853, 2), 19467, 40]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3²³⁷, 9852, F₃, 2, 39) (dual of [(9852, 2), 19467, 40]-NRT-code), using

OOA 2-folding [i] 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, 9845, F₃, 3, 39) (dual of [(9845, 3), 29296, 40]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²³⁹, 9845, F₃, 4, 39) (dual of [(9845, 4), 39141, 40]-NRT-code)	[i]
3	Linear OOA(3²³⁹, 9845, F₃, 5, 39) (dual of [(9845, 5), 48986, 40]-NRT-code)	[i]
4	Digital (200, 239, 9845)-net over F₃	[i]