MinT - Information on Result #2628352

Information on Result #2628352

Linear OOA(3²³⁷, 1594346, F₃, 3, 24) (dual of [(1594346, 3), 4782801, 25]-NRT-code), using strength reduction based on linear OOA(3²³⁷, 1594346, F₃, 3, 25) (dual of [(1594346, 3), 4782801, 26]-NRT-code), using

OOA 3-folding [i] based on linear OA(3²³⁷, 4783038, F₃, 25) (dual of [4783038, 4782801, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3²³⁶, 4783037, F₃, 25) (dual of [4783037, 4782801, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. linear OA(3²²⁵, 4782970, F₃, 25) (dual of [4782970, 4782745, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. linear OA(3¹⁶⁹, 4782970, F₃, 19) (dual of [4782970, 4782801, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970Â | 3²⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(3¹¹, 67, F₃, 5) (dual of [67, 56, 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(3²³⁸, 1594346, F₃, 3, 24) (dual of [(1594346, 3), 4782800, 25]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3²³⁹, 1594346, F₃, 3, 24) (dual of [(1594346, 3), 4782799, 25]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²³⁷, 1587047, F₃, 4, 24) (dual of [(1587047, 4), 6347951, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3²³⁷, 1587047, F₃, 5, 24) (dual of [(1587047, 5), 7934998, 25]-NRT-code)	[i]
5	Digital (213, 237, 1587047)-net over F₃	[i]