MinT - Information on Result #2487304

Information on Result #2487304

Linear OOA(3²⁰⁵, 29551, F₃, 2, 29) (dual of [(29551, 2), 58897, 30]-NRT-code), using 3¹ times duplication based on linear OOA(3²⁰⁴, 29551, F₃, 2, 29) (dual of [(29551, 2), 58898, 30]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3²⁰², 29550, F₃, 2, 29) (dual of [(29550, 2), 58898, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²⁰², 59100, F₃, 29) (dual of [59100, 58898, 30]-code), using
  - constructionÂ X applied to C_e(28) âŠ‚ C_e(22) [i] based on
    1. linear OA(3¹⁹¹, 59049, F₃, 29) (dual of [59049, 58858, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(3¹¹, 51, F₃, 5) (dual of [51, 40, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3²⁰⁵, 27996, F₃, 3, 29) (dual of [(27996, 3), 83783, 30]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁰⁵, 27996, F₃, 4, 29) (dual of [(27996, 4), 111779, 30]-NRT-code)	[i]
3	Linear OOA(3²⁰⁵, 27996, F₃, 5, 29) (dual of [(27996, 5), 139775, 30]-NRT-code)	[i]
4	Digital (176, 205, 27996)-net over F₃	[i]