MinT - Information on Result #813908

Information on Result #813908

Linear OOA(3¹¹⁹, 3292, F₃, 2, 22) (dual of [(3292, 2), 6465, 23]-NRT-code), using OOA 2-folding based on linear OA(3¹¹⁹, 6584, F₃, 22) (dual of [6584, 6465, 23]-code), using

constructionÂ XX applied to C_e(21) âŠ‚ C_e(18) âŠ‚ C_e(16) [i] based on
1. linear OA(3¹¹³, 6561, F₃, 22) (dual of [6561, 6448, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
2. linear OA(3⁹⁷, 6561, F₃, 19) (dual of [6561, 6464, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
3. linear OA(3⁸⁹, 6561, F₃, 17) (dual of [6561, 6472, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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(3¹¹⁹, 3292, F₃, 3, 22) (dual of [(3292, 3), 9757, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹¹⁹, 3292, F₃, 4, 22) (dual of [(3292, 4), 13049, 23]-NRT-code)	[i]
3	Linear OOA(3¹¹⁹, 3292, F₃, 5, 22) (dual of [(3292, 5), 16341, 23]-NRT-code)	[i]
4	Digital (97, 119, 3292)-net over F₃	[i]