MinT - Information on Result #814750

Information on Result #814750

Linear OOA(3¹⁹², 29550, F₃, 2, 28) (dual of [(29550, 2), 58908, 29]-NRT-code), using OOA 2-folding based on linear OA(3¹⁹², 59100, F₃, 28) (dual of [59100, 58908, 29]-code), using

constructionÂ X applied to C_e(27) âŠ‚ C_e(21) [i] based on
1. linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
2. linear OA(3¹⁴¹, 59049, F₃, 22) (dual of [59049, 58908, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [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(3¹⁹², 29550, F₃, 2, 27) (dual of [(29550, 2), 58908, 28]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(3¹⁹⁴, 29551, F₃, 2, 28) (dual of [(29551, 2), 58908, 29]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(3¹⁹⁶, 29552, F₃, 2, 28) (dual of [(29552, 2), 58908, 29]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
4	Linear OOA(3¹⁹³, 29550, F₃, 2, 28) (dual of [(29550, 2), 58907, 29]-NRT-code)	[i]	OOA Duplication
5	Linear OOA(3¹⁹¹, 29549, F₃, 2, 27) (dual of [(29549, 2), 58907, 28]-NRT-code)	[i]	Truncation for OOAs
6	Linear OOA(3¹⁹², 21490, F₃, 3, 28) (dual of [(21490, 3), 64278, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
7	Linear OOA(3¹⁹², 21490, F₃, 4, 28) (dual of [(21490, 4), 85768, 29]-NRT-code)	[i]
8	Linear OOA(3¹⁹², 21490, F₃, 5, 28) (dual of [(21490, 5), 107258, 29]-NRT-code)	[i]
9	Digital (164, 192, 21490)-net over F₃	[i]