MinT - Information on Result #813924

Information on Result #813924

Linear OOA(3¹³⁸, 9865, F₃, 2, 22) (dual of [(9865, 2), 19592, 23]-NRT-code), using OOA 2-folding based on linear OA(3¹³⁸, 19730, F₃, 22) (dual of [19730, 19592, 23]-code), using

constructionÂ X applied to C_e(21) âŠ‚ C_e(15) [i] based on
1. linear OA(3¹²⁷, 19683, F₃, 22) (dual of [19683, 19556, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
2. linear OA(3⁹¹, 19683, F₃, 16) (dual of [19683, 19592, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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(3¹³⁸, 9865, F₃, 2, 21) (dual of [(9865, 2), 19592, 22]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁴⁰, 9866, F₃, 2, 22) (dual of [(9866, 2), 19592, 23]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3¹³⁹, 9865, F₃, 2, 22) (dual of [(9865, 2), 19591, 23]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3¹³⁷, 9864, F₃, 2, 21) (dual of [(9864, 2), 19591, 22]-NRT-code)	[i]	Truncation for OOAs
5	Linear OOA(3¹³⁸, 9865, F₃, 3, 22) (dual of [(9865, 3), 29457, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
6	Linear OOA(3¹³⁸, 9865, F₃, 4, 22) (dual of [(9865, 4), 39322, 23]-NRT-code)	[i]
7	Linear OOA(3¹³⁸, 9865, F₃, 5, 22) (dual of [(9865, 5), 49187, 23]-NRT-code)	[i]
8	Digital (116, 138, 9865)-net over F₃	[i]