MinT - Information on Result #815530

Information on Result #815530

Linear OOA(3²⁰⁷, 9859, F₃, 2, 34) (dual of [(9859, 2), 19511, 35]-NRT-code), using OOA 2-folding based on linear OA(3²⁰⁷, 19718, F₃, 34) (dual of [19718, 19511, 35]-code), using

constructionÂ X applied to C_e(33) âŠ‚ C_e(28) [i] based on
1. 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]
2. linear OA(3¹⁷², 19683, F₃, 29) (dual of [19683, 19511, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(3²⁰⁸, 9859, F₃, 2, 34) (dual of [(9859, 2), 19510, 35]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3²⁰⁶, 9858, F₃, 2, 33) (dual of [(9858, 2), 19510, 34]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(3²⁰⁷, 8845, F₃, 3, 34) (dual of [(8845, 3), 26328, 35]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3²⁰⁷, 8845, F₃, 4, 34) (dual of [(8845, 4), 35173, 35]-NRT-code)	[i]
5	Linear OOA(3²⁰⁷, 8845, F₃, 5, 34) (dual of [(8845, 5), 44018, 35]-NRT-code)	[i]
6	Digital (173, 207, 8845)-net over F₃	[i]