MinT - Information on Result #815514

Information on Result #815514

Linear OOA(3¹⁸³, 3292, F₃, 2, 34) (dual of [(3292, 2), 6401, 35]-NRT-code), using OOA 2-folding based on linear OA(3¹⁸³, 6584, F₃, 34) (dual of [6584, 6401, 35]-code), using

constructionÂ XX applied to C_e(33) âŠ‚ C_e(30) âŠ‚ C_e(28) [i] based on
1. linear OA(3¹⁷⁷, 6561, F₃, 34) (dual of [6561, 6384, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
2. linear OA(3¹⁶¹, 6561, F₃, 31) (dual of [6561, 6400, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
3. linear OA(3¹⁵³, 6561, F₃, 29) (dual of [6561, 6408, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
4. linear OA(3⁴, 21, F₃, 2) (dual of [21, 17, 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]
5. linear OA(3¹, 2, F₃, 1) (dual of [2, 1, 2]-code), using
  - dual of repetition code with length 2 [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(3¹⁸³, 3292, F₃, 3, 34) (dual of [(3292, 3), 9693, 35]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸³, 3292, F₃, 4, 34) (dual of [(3292, 4), 12985, 35]-NRT-code)	[i]
3	Linear OOA(3¹⁸³, 3292, F₃, 5, 34) (dual of [(3292, 5), 16277, 35]-NRT-code)	[i]
4	Digital (149, 183, 3292)-net over F₃	[i]