MinT - Information on Result #815146

Information on Result #815146

Linear OOA(3¹⁸⁹, 9859, F₃, 2, 31) (dual of [(9859, 2), 19529, 32]-NRT-code), using OOA 2-folding based on linear OA(3¹⁸⁹, 19718, F₃, 31) (dual of [19718, 19529, 32]-code), using

constructionÂ X applied to C_e(30) âŠ‚ C_e(25) [i] based on
1. linear OA(3¹⁸¹, 19683, F₃, 31) (dual of [19683, 19502, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
2. linear OA(3¹⁵⁴, 19683, F₃, 26) (dual of [19683, 19529, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
3. linear OA(3⁸, 35, F₃, 4) (dual of [35, 27, 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(3¹⁹⁰, 9859, F₃, 2, 31) (dual of [(9859, 2), 19528, 32]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁸⁸, 9858, F₃, 2, 30) (dual of [(9858, 2), 19528, 31]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(3¹⁸⁹, 8652, F₃, 3, 31) (dual of [(8652, 3), 25767, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3¹⁸⁹, 8652, F₃, 4, 31) (dual of [(8652, 4), 34419, 32]-NRT-code)	[i]
5	Linear OOA(3¹⁸⁹, 8652, F₃, 5, 31) (dual of [(8652, 5), 43071, 32]-NRT-code)	[i]
6	Digital (158, 189, 8652)-net over F₃	[i]