MinT - Information on Result #816284

Information on Result #816284

Linear OOA(3²⁴⁶, 9865, F₃, 2, 40) (dual of [(9865, 2), 19484, 41]-NRT-code), using OOA 2-folding based on linear OA(3²⁴⁶, 19730, F₃, 40) (dual of [19730, 19484, 41]-code), using

constructionÂ X applied to C_e(39) âŠ‚ C_e(33) [i] based on
1. linear OA(3²³⁵, 19683, F₃, 40) (dual of [19683, 19448, 41]-code), using an extension C_e(39) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,39], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 40 [i]
2. linear OA(3¹⁹⁹, 19683, F₃, 34) (dual of [19683, 19484, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
3. linear OA(3¹¹, 47, F₃, 5) (dual of [47, 36, 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(3²⁴⁶, 9865, F₃, 2, 39) (dual of [(9865, 2), 19484, 40]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3²⁴⁸, 9866, F₃, 2, 40) (dual of [(9866, 2), 19484, 41]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3²⁵⁰, 9867, F₃, 2, 40) (dual of [(9867, 2), 19484, 41]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
4	Linear OOA(3²⁴⁷, 9865, F₃, 2, 40) (dual of [(9865, 2), 19483, 41]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(3²⁴⁵, 9864, F₃, 2, 39) (dual of [(9864, 2), 19483, 40]-NRT-code)	[i]	Truncation for OOAs
6	Linear OOA(3²⁴⁶, 9865, F₃, 3, 40) (dual of [(9865, 3), 29349, 41]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
7	Linear OOA(3²⁴⁶, 9865, F₃, 4, 40) (dual of [(9865, 4), 39214, 41]-NRT-code)	[i]
8	Linear OOA(3²⁴⁶, 9865, F₃, 5, 40) (dual of [(9865, 5), 49079, 41]-NRT-code)	[i]
9	Digital (206, 246, 9865)-net over F₃	[i]