MinT - Information on Result #815903

Information on Result #815903

Linear OOA(3²²⁵, 9859, F₃, 2, 37) (dual of [(9859, 2), 19493, 38]-NRT-code), using OOA 2-folding based on linear OA(3²²⁵, 19718, F₃, 37) (dual of [19718, 19493, 38]-code), using

constructionÂ X applied to C_e(36) âŠ‚ C_e(31) [i] based on
1. linear OA(3²¹⁷, 19683, F₃, 37) (dual of [19683, 19466, 38]-code), using an extension C_e(36) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,36], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 37 [i]
2. linear OA(3¹⁹⁰, 19683, F₃, 32) (dual of [19683, 19493, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [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(3²²⁶, 9859, F₃, 2, 37) (dual of [(9859, 2), 19492, 38]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3²²⁴, 9858, F₃, 2, 36) (dual of [(9858, 2), 19492, 37]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(3²²⁵, 9083, F₃, 3, 37) (dual of [(9083, 3), 27024, 38]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3²²⁵, 9083, F₃, 4, 37) (dual of [(9083, 4), 36107, 38]-NRT-code)	[i]
5	Linear OOA(3²²⁵, 9083, F₃, 5, 37) (dual of [(9083, 5), 45190, 38]-NRT-code)	[i]
6	Digital (188, 225, 9083)-net over F₃	[i]