MinT - Information on Result #813820

Information on Result #813820

Linear OOA(3¹⁸¹, 265751, F₃, 2, 21) (dual of [(265751, 2), 531321, 22]-NRT-code), using OOA 2-folding based on linear OA(3¹⁸¹, 531502, F₃, 21) (dual of [531502, 531321, 22]-code), using

1 times code embedding in larger space [i] based on linear OA(3¹⁸⁰, 531501, F₃, 21) (dual of [531501, 531321, 22]-code), using
- constructionÂ X applied to C([0,10]) âŠ‚ C([0,7]) [i] based on
  1. linear OA(3¹⁶⁹, 531442, F₃, 21) (dual of [531442, 531273, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
  2. linear OA(3¹²¹, 531442, F₃, 15) (dual of [531442, 531321, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]
  3. linear OA(3¹¹, 59, F₃, 5) (dual of [59, 48, 6]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
      - codes constructed by inverting constructionÂ Y₁ [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(3¹⁸¹, 209783, F₃, 3, 21) (dual of [(209783, 3), 629168, 22]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸¹, 209783, F₃, 4, 21) (dual of [(209783, 4), 838951, 22]-NRT-code)	[i]
3	Linear OOA(3¹⁸¹, 209783, F₃, 5, 21) (dual of [(209783, 5), 1048734, 22]-NRT-code)	[i]
4	Digital (160, 181, 209783)-net over F₃	[i]