MinT - Information on Result #814608

Information on Result #814608

Linear OOA(3¹⁸⁸, 29543, F₃, 2, 27) (dual of [(29543, 2), 58898, 28]-NRT-code), using OOA 2-folding based on linear OA(3¹⁸⁸, 59086, F₃, 27) (dual of [59086, 58898, 28]-code), using

1 times truncation [i] based on linear OA(3¹⁸⁹, 59087, F₃, 28) (dual of [59087, 58898, 29]-code), using
- constructionÂ X applied to C_e(27) âŠ‚ C_e(22) [i] based on
  1. linear OA(3¹⁸¹, 59049, F₃, 28) (dual of [59049, 58868, 29]-code), using an extension C_e(27) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,27], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 28 [i]
  2. linear OA(3¹⁵¹, 59049, F₃, 23) (dual of [59049, 58898, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
  3. linear OA(3⁸, 38, F₃, 4) (dual of [38, 30, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁸, 41, F₃, 4) (dual of [41, 33, 5]-code), using
      - the narrow-sense BCH-code C(I) with length 41Â | 3⁸âˆ’1, defining interval IÂ =Â [1,1], and minimum distance dÂ â‰¥ |{−3,−1,1,3}|+1Â =Â 5 (BCH-bound) [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(3¹⁸⁸, 24413, F₃, 3, 27) (dual of [(24413, 3), 73051, 28]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸⁸, 24413, F₃, 4, 27) (dual of [(24413, 4), 97464, 28]-NRT-code)	[i]
3	Linear OOA(3¹⁸⁸, 24413, F₃, 5, 27) (dual of [(24413, 5), 121877, 28]-NRT-code)	[i]
4	Digital (161, 188, 24413)-net over F₃	[i]