MinT - Information on Result #2266785

Information on Result #2266785

Linear OA(3²¹⁸, 6602, F₃, 39) (dual of [6602, 6384, 40]-code), using 1 times code embedding in larger space based on linear OA(3²¹⁷, 6601, F₃, 39) (dual of [6601, 6384, 40]-code), using

constructionÂ X applied to C_e(39) âŠ‚ C_e(33) [i] based on
1. linear OA(3²⁰⁹, 6561, F₃, 40) (dual of [6561, 6352, 41]-code), using an extension C_e(39) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,39], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 40 [i]
2. linear OA(3¹⁷⁷, 6561, F₃, 34) (dual of [6561, 6384, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [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(3²¹⁸, 4569, F₃, 2, 39) (dual of [(4569, 2), 8920, 40]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²¹⁸, 4569, F₃, 3, 39) (dual of [(4569, 3), 13489, 40]-NRT-code)	[i]
3	Linear OOA(3²¹⁸, 4569, F₃, 4, 39) (dual of [(4569, 4), 18058, 40]-NRT-code)	[i]
4	Linear OOA(3²¹⁸, 4569, F₃, 5, 39) (dual of [(4569, 5), 22627, 40]-NRT-code)	[i]
5	Digital (179, 218, 4569)-net over F₃	[i]
6	Linear OOA(3²¹⁸, 3301, F₃, 2, 39) (dual of [(3301, 2), 6384, 40]-NRT-code)	[i]	OOA Folding