MinT - Information on Result #814301

Information on Result #814301

Linear OOA(3¹⁴⁹, 9852, F₃, 2, 25) (dual of [(9852, 2), 19555, 26]-NRT-code), using OOA 2-folding based on linear OA(3¹⁴⁹, 19704, F₃, 25) (dual of [19704, 19555, 26]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁴⁹, 19705, F₃, 25) (dual of [19705, 19556, 26]-code), using
- constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
  1. linear OA(3¹⁴⁵, 19683, F₃, 25) (dual of [19683, 19538, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
  2. linear OA(3¹²⁷, 19683, F₃, 22) (dual of [19683, 19556, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
  3. linear OA(3⁴, 22, F₃, 2) (dual of [22, 18, 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(3¹⁴⁹, 6959, F₃, 3, 25) (dual of [(6959, 3), 20728, 26]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁴⁹, 6959, F₃, 4, 25) (dual of [(6959, 4), 27687, 26]-NRT-code)	[i]
3	Linear OOA(3¹⁴⁹, 6959, F₃, 5, 25) (dual of [(6959, 5), 34646, 26]-NRT-code)	[i]
4	Digital (124, 149, 6959)-net over F₃	[i]