MinT - Information on Result #952861

Information on Result #952861

Linear OOA(3¹⁶⁶, 531457, F₃, 3, 19) (dual of [(531457, 3), 1594205, 20]-NRT-code), using OOA 3-folding based on linear OA(3¹⁶⁶, 1594371, F₃, 19) (dual of [1594371, 1594205, 20]-code), using

constructionÂ X applied to C_e(18) âŠ‚ C_e(13) [i] based on
1. linear OA(3¹⁵⁷, 1594323, F₃, 19) (dual of [1594323, 1594166, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
2. linear OA(3¹¹⁸, 1594323, F₃, 14) (dual of [1594323, 1594205, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 1594322Â = 3¹³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
3. linear OA(3⁹, 48, F₃, 4) (dual of [48, 39, 5]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
    - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(3¹⁶⁷, 531457, F₃, 3, 19) (dual of [(531457, 3), 1594204, 20]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3¹⁶⁵, 531456, F₃, 3, 18) (dual of [(531456, 3), 1594203, 19]-NRT-code)	[i]	Truncation for OOAs
3	Linear OOA(3¹⁶⁶, 491408, F₃, 4, 19) (dual of [(491408, 4), 1965466, 20]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3¹⁶⁶, 491408, F₃, 5, 19) (dual of [(491408, 5), 2456874, 20]-NRT-code)	[i]
5	Digital (147, 166, 491408)-net over F₃	[i]