MinT - Information on Result #814580

Information on Result #814580

Linear OOA(3¹⁴⁷, 3290, F₃, 2, 27) (dual of [(3290, 2), 6433, 28]-NRT-code), using OOA 2-folding based on linear OA(3¹⁴⁷, 6580, F₃, 27) (dual of [6580, 6433, 28]-code), using

1 times code embedding in larger space [i] based on linear OA(3¹⁴⁶, 6579, F₃, 27) (dual of [6579, 6433, 28]-code), using
- constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
  1. linear OA(3¹⁴⁵, 6562, F₃, 27) (dual of [6562, 6417, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
  2. linear OA(3¹²⁹, 6562, F₃, 25) (dual of [6562, 6433, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562Â | 3¹⁶âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
  3. linear OA(3¹, 17, F₃, 1) (dual of [17, 16, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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(3¹⁴⁹, 3291, F₃, 2, 27) (dual of [(3291, 2), 6433, 28]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(3¹⁴⁸, 3290, F₃, 2, 27) (dual of [(3290, 2), 6432, 28]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(3¹⁴⁷, 3290, F₃, 3, 27) (dual of [(3290, 3), 9723, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
4	Linear OOA(3¹⁴⁷, 3290, F₃, 4, 27) (dual of [(3290, 4), 13013, 28]-NRT-code)	[i]
5	Linear OOA(3¹⁴⁷, 3290, F₃, 5, 27) (dual of [(3290, 5), 16303, 28]-NRT-code)	[i]
6	Digital (120, 147, 3290)-net over F₃	[i]