MinT - Information on Result #814724

Information on Result #814724

Linear OOA(3¹⁵⁰, 3291, F₃, 2, 28) (dual of [(3291, 2), 6432, 29]-NRT-code), using OOA 2-folding based on linear OA(3¹⁵⁰, 6582, F₃, 28) (dual of [6582, 6432, 29]-code), using

1 times code embedding in larger space [i] based on linear OA(3¹⁴⁹, 6581, F₃, 28) (dual of [6581, 6432, 29]-code), using
- constructionÂ X applied to C_e(27) âŠ‚ C_e(24) [i] based on
  1. linear OA(3¹⁴⁵, 6561, F₃, 28) (dual of [6561, 6416, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
  2. linear OA(3¹²⁹, 6561, F₃, 25) (dual of [6561, 6432, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 3⁸âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
  3. linear OA(3⁴, 20, F₃, 2) (dual of [20, 16, 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]

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(3¹⁵⁰, 3291, F₃, 3, 28) (dual of [(3291, 3), 9723, 29]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁵⁰, 3291, F₃, 4, 28) (dual of [(3291, 4), 13014, 29]-NRT-code)	[i]
3	Linear OOA(3¹⁵⁰, 3291, F₃, 5, 28) (dual of [(3291, 5), 16305, 29]-NRT-code)	[i]
4	Digital (122, 150, 3291)-net over F₃	[i]