MinT - Information on Result #815161

Information on Result #815161

Linear OOA(3²¹⁸, 29558, F₃, 2, 31) (dual of [(29558, 2), 58898, 32]-NRT-code), using OOA 2-folding based on linear OA(3²¹⁸, 59116, F₃, 31) (dual of [59116, 58898, 32]-code), using

constructionÂ X applied to C_e(30) âŠ‚ C_e(22) [i] based on
1. linear OA(3²⁰¹, 59049, F₃, 31) (dual of [59049, 58848, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
2. linear OA(3¹⁵¹, 59049, F₃, 23) (dual of [59049, 58898, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
3. linear OA(3¹⁷, 67, F₃, 7) (dual of [67, 50, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁷, 80, F₃, 7) (dual of [80, 63, 8]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [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(3²²⁰, 29559, F₃, 2, 31) (dual of [(29559, 2), 58898, 32]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3²¹⁹, 29558, F₃, 2, 31) (dual of [(29558, 2), 58897, 32]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²¹⁸, 27052, F₃, 3, 31) (dual of [(27052, 3), 80938, 32]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3²¹⁸, 27052, F₃, 4, 31) (dual of [(27052, 4), 107990, 32]-NRT-code)	[i]
5	Linear OOA(3²¹⁸, 27052, F₃, 5, 31) (dual of [(27052, 5), 135042, 32]-NRT-code)	[i]
6	Digital (187, 218, 27052)-net over F₃	[i]