MinT - Information on Result #2267109

Information on Result #2267109

Linear OA(3²⁴⁶, 6582, F₃, 46) (dual of [6582, 6336, 47]-code), using 1 times code embedding in larger space based on linear OA(3²⁴⁵, 6581, F₃, 46) (dual of [6581, 6336, 47]-code), using

constructionÂ X applied to C_e(45) âŠ‚ C_e(42) [i] based on
1. linear OA(3²⁴¹, 6561, F₃, 46) (dual of [6561, 6320, 47]-code), using an extension C_e(45) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,45], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 46 [i]
2. linear OA(3²²⁵, 6561, F₃, 43) (dual of [6561, 6336, 44]-code), using an extension C_e(42) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,42], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 43 [i]
3. linear OA(3⁴, 20, F₃, 2) (dual of [20, 16, 3]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
    - Hamming code H(4,3) [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(3²⁴⁶, 3872, F₃, 2, 46) (dual of [(3872, 2), 7498, 47]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁴⁶, 3872, F₃, 3, 46) (dual of [(3872, 3), 11370, 47]-NRT-code)	[i]
3	Linear OOA(3²⁴⁶, 3872, F₃, 4, 46) (dual of [(3872, 4), 15242, 47]-NRT-code)	[i]
4	Linear OOA(3²⁴⁶, 3872, F₃, 5, 46) (dual of [(3872, 5), 19114, 47]-NRT-code)	[i]
5	Digital (200, 246, 3872)-net over F₃	[i]
6	Linear OOA(3²⁴⁶, 3291, F₃, 2, 46) (dual of [(3291, 2), 6336, 47]-NRT-code)	[i]	OOA Folding
7	Linear OOA(3²⁴⁶, 2194, F₃, 3, 46) (dual of [(2194, 3), 6336, 47]-NRT-code)	[i]	OOA Folding