MinT - Information on Result #814162

Information on Result #814162

Linear OOA(3¹⁴⁹, 9853, F₃, 2, 24) (dual of [(9853, 2), 19557, 25]-NRT-code), using OOA 2-folding based on linear OA(3¹⁴⁹, 19706, F₃, 24) (dual of [19706, 19557, 25]-code), using

constructionÂ X applied to C([0,12]) âŠ‚ C([0,10]) [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(3¹²⁷, 19684, F₃, 21) (dual of [19684, 19557, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 3¹⁸âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [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(3¹⁴⁹, 9471, F₃, 3, 24) (dual of [(9471, 3), 28264, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁴⁹, 9471, F₃, 4, 24) (dual of [(9471, 4), 37735, 25]-NRT-code)	[i]
3	Linear OOA(3¹⁴⁹, 9471, F₃, 5, 24) (dual of [(9471, 5), 47206, 25]-NRT-code)	[i]
4	Digital (125, 149, 9471)-net over F₃	[i]