MinT - Information on Result #2266250

Information on Result #2266250

Linear OA(3¹⁷⁰, 6603, F₃, 30) (dual of [6603, 6433, 31]-code), using 1 times code embedding in larger space based on linear OA(3¹⁶⁹, 6602, F₃, 30) (dual of [6602, 6433, 31]-code), using

constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
1. linear OA(3¹⁶¹, 6562, F₃, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
2. linear OA(3¹²⁹, 6562, F₃, 25) (dual of [6562, 6433, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
3. linear OA(3⁸, 40, F₃, 4) (dual of [40, 32, 5]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
    - the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [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(3¹⁷⁰, 4256, F₃, 2, 30) (dual of [(4256, 2), 8342, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁷⁰, 4256, F₃, 3, 30) (dual of [(4256, 3), 12598, 31]-NRT-code)	[i]
3	Linear OOA(3¹⁷⁰, 4256, F₃, 4, 30) (dual of [(4256, 4), 16854, 31]-NRT-code)	[i]
4	Linear OOA(3¹⁷⁰, 4256, F₃, 5, 30) (dual of [(4256, 5), 21110, 31]-NRT-code)	[i]
5	Digital (140, 170, 4256)-net over F₃	[i]
6	Linear OOA(3¹⁷⁰, 2201, F₃, 3, 30) (dual of [(2201, 3), 6433, 31]-NRT-code)	[i]	OOA Folding