MinT - Information on Result #814305

Information on Result #814305

Linear OOA(3¹⁵³, 9859, F₃, 2, 25) (dual of [(9859, 2), 19565, 26]-NRT-code), using OOA 2-folding based on linear OA(3¹⁵³, 19718, F₃, 25) (dual of [19718, 19565, 26]-code), using

constructionÂ X applied to C_e(24) âŠ‚ C_e(19) [i] based on
1. linear OA(3¹⁴⁵, 19683, F₃, 25) (dual of [19683, 19538, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
2. linear OA(3¹¹⁸, 19683, F₃, 20) (dual of [19683, 19565, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [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(3¹⁵⁴, 9859, F₃, 2, 25) (dual of [(9859, 2), 19564, 26]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁵², 9858, F₃, 2, 24) (dual of [(9858, 2), 19564, 25]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(3¹⁵³, 8502, F₃, 3, 25) (dual of [(8502, 3), 25353, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3¹⁵³, 8502, F₃, 4, 25) (dual of [(8502, 4), 33855, 26]-NRT-code)	[i]
5	Linear OOA(3¹⁵³, 8502, F₃, 5, 25) (dual of [(8502, 5), 42357, 26]-NRT-code)	[i]
6	Digital (128, 153, 8502)-net over F₃	[i]