MinT - Information on Result #813259

Information on Result #813259

Linear OOA(3⁹⁹, 9859, F₃, 2, 16) (dual of [(9859, 2), 19619, 17]-NRT-code), using OOA 2-folding based on linear OA(3⁹⁹, 19718, F₃, 16) (dual of [19718, 19619, 17]-code), using

constructionÂ X applied to C_e(15) âŠ‚ C_e(10) [i] based on
1. linear OA(3⁹¹, 19683, F₃, 16) (dual of [19683, 19592, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
2. linear OA(3⁶⁴, 19683, F₃, 11) (dual of [19683, 19619, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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(3¹⁰⁰, 9859, F₃, 2, 16) (dual of [(9859, 2), 19618, 17]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3⁹⁸, 9858, F₃, 2, 15) (dual of [(9858, 2), 19618, 16]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(3⁹⁹, 9859, F₃, 3, 16) (dual of [(9859, 3), 29478, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3⁹⁹, 9859, F₃, 4, 16) (dual of [(9859, 4), 39337, 17]-NRT-code)	[i]
5	Linear OOA(3⁹⁹, 9859, F₃, 5, 16) (dual of [(9859, 5), 49196, 17]-NRT-code)	[i]
6	Digital (83, 99, 9859)-net over F₃	[i]