MinT - Information on Result #814166

Information on Result #814166

Linear OOA(3¹⁵⁴, 9864, F₃, 2, 24) (dual of [(9864, 2), 19574, 25]-NRT-code), using OOA 2-folding based on linear OA(3¹⁵⁴, 19728, F₃, 24) (dual of [19728, 19574, 25]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁵⁴, 19729, F₃, 24) (dual of [19729, 19575, 25]-code), using
- constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
  1. linear OA(3¹⁴⁵, 19684, F₃, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
  2. linear OA(3¹⁰⁹, 19684, F₃, 19) (dual of [19684, 19575, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
  3. linear OA(3⁹, 45, F₃, 4) (dual of [45, 36, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(3¹⁵⁴, 9864, F₃, 3, 24) (dual of [(9864, 3), 29438, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁵⁴, 9864, F₃, 4, 24) (dual of [(9864, 4), 39302, 25]-NRT-code)	[i]
3	Linear OOA(3¹⁵⁴, 9864, F₃, 5, 24) (dual of [(9864, 5), 49166, 25]-NRT-code)	[i]
4	Digital (130, 154, 9864)-net over F₃	[i]