MinT - Information on Result #814896

Information on Result #814896

Linear OOA(3²²⁶, 88609, F₃, 2, 29) (dual of [(88609, 2), 176992, 30]-NRT-code), using OOA 2-folding based on linear OA(3²²⁶, 177218, F₃, 29) (dual of [177218, 176992, 30]-code), using

constructionÂ X applied to C_e(28) âŠ‚ C_e(21) [i] based on
1. linear OA(3²¹⁰, 177147, F₃, 29) (dual of [177147, 176937, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
2. linear OA(3¹⁵⁵, 177147, F₃, 22) (dual of [177147, 176992, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
3. linear OA(3¹⁶, 71, F₃, 6) (dual of [71, 55, 7]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹⁶, 80, F₃, 6) (dual of [80, 64, 7]-code), using
    - the primitive narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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(3²²⁸, 88610, F₃, 2, 29) (dual of [(88610, 2), 176992, 30]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3²²⁷, 88609, F₃, 2, 29) (dual of [(88609, 2), 176991, 30]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3²²⁶, 68028, F₃, 3, 29) (dual of [(68028, 3), 203858, 30]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3²²⁶, 68028, F₃, 4, 29) (dual of [(68028, 4), 271886, 30]-NRT-code)	[i]
5	Linear OOA(3²²⁶, 68028, F₃, 5, 29) (dual of [(68028, 5), 339914, 30]-NRT-code)	[i]
6	Digital (197, 226, 68028)-net over F₃	[i]