MinT - Information on Result #813569

Information on Result #813569

Linear OOA(3¹¹⁷, 9859, F₃, 2, 19) (dual of [(9859, 2), 19601, 20]-NRT-code), using OOA 2-folding based on linear OA(3¹¹⁷, 19718, F₃, 19) (dual of [19718, 19601, 20]-code), using

constructionÂ X applied to C_e(18) âŠ‚ C_e(13) [i] based on
1. linear OA(3¹⁰⁹, 19683, F₃, 19) (dual of [19683, 19574, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
2. linear OA(3⁸², 19683, F₃, 14) (dual of [19683, 19601, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [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(3¹¹⁸, 9859, F₃, 2, 19) (dual of [(9859, 2), 19600, 20]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹¹⁶, 9858, F₃, 2, 18) (dual of [(9858, 2), 19600, 19]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(3¹¹⁷, 9122, F₃, 3, 19) (dual of [(9122, 3), 27249, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3¹¹⁷, 9122, F₃, 4, 19) (dual of [(9122, 4), 36371, 20]-NRT-code)	[i]
5	Linear OOA(3¹¹⁷, 9122, F₃, 5, 19) (dual of [(9122, 5), 45493, 20]-NRT-code)	[i]
6	Digital (98, 117, 9122)-net over F₃	[i]