MinT - Information on Result #952549

Information on Result #952549

Linear OOA(3¹⁰⁵, 19691, F₃, 3, 16) (dual of [(19691, 3), 58968, 17]-NRT-code), using OOA 3-folding based on linear OA(3¹⁰⁵, 59073, F₃, 16) (dual of [59073, 58968, 17]-code), using

constructionÂ X applied to C_e(15) âŠ‚ C_e(12) [i] based on
1. linear OA(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [i]
2. linear OA(3⁸¹, 59049, F₃, 13) (dual of [59049, 58968, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
3. linear OA(3⁴, 24, F₃, 2) (dual of [24, 20, 3]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
    - Hamming code H(4,3) [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(3¹⁰⁵, 19691, F₃, 3, 15) (dual of [(19691, 3), 58968, 16]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁰⁸, 19692, F₃, 3, 16) (dual of [(19692, 3), 58968, 17]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3¹⁰⁶, 19691, F₃, 3, 16) (dual of [(19691, 3), 58967, 17]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(3¹⁰⁷, 19691, F₃, 3, 16) (dual of [(19691, 3), 58966, 17]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(3¹⁰⁵, 19691, F₃, 4, 16) (dual of [(19691, 4), 78659, 17]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
6	Linear OOA(3¹⁰⁵, 19691, F₃, 5, 16) (dual of [(19691, 5), 98350, 17]-NRT-code)	[i]
7	Digital (89, 105, 19691)-net over F₃	[i]