MinT - Information on Result #813477

Information on Result #813477

Linear OOA(3¹⁵⁴, 265749, F₃, 2, 18) (dual of [(265749, 2), 531344, 19]-NRT-code), using OOA 2-folding based on linear OA(3¹⁵⁴, 531498, F₃, 18) (dual of [531498, 531344, 19]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁵⁴, 531499, F₃, 18) (dual of [531499, 531345, 19]-code), using
- constructionÂ X applied to C([0,9]) âŠ‚ C([0,6]) [i] based on
  1. linear OA(3¹⁴⁵, 531442, F₃, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
  2. linear OA(3⁹⁷, 531442, F₃, 13) (dual of [531442, 531345, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
  3. linear OA(3⁹, 57, F₃, 4) (dual of [57, 48, 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, 219552, F₃, 3, 18) (dual of [(219552, 3), 658502, 19]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁵⁴, 219552, F₃, 4, 18) (dual of [(219552, 4), 878054, 19]-NRT-code)	[i]
3	Linear OOA(3¹⁵⁴, 219552, F₃, 5, 18) (dual of [(219552, 5), 1097606, 19]-NRT-code)	[i]
4	Digital (136, 154, 219552)-net over F₃	[i]