MinT - Information on Result #815540

Information on Result #815540

Linear OOA(3²³⁰, 29544, F₃, 2, 34) (dual of [(29544, 2), 58858, 35]-NRT-code), using OOA 2-folding based on linear OA(3²³⁰, 59088, F₃, 34) (dual of [59088, 58858, 35]-code), using

1 times code embedding in larger space [i] based on linear OA(3²²⁹, 59087, F₃, 34) (dual of [59087, 58858, 35]-code), using
- constructionÂ X applied to C_e(33) âŠ‚ C_e(28) [i] based on
  1. linear OA(3²²¹, 59049, F₃, 34) (dual of [59049, 58828, 35]-code), using an extension C_e(33) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,33], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 34 [i]
  2. linear OA(3¹⁹¹, 59049, F₃, 29) (dual of [59049, 58858, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [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(3²³¹, 29544, F₃, 2, 34) (dual of [(29544, 2), 58857, 35]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(3²³⁰, 20022, F₃, 3, 34) (dual of [(20022, 3), 59836, 35]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
3	Linear OOA(3²³⁰, 20022, F₃, 4, 34) (dual of [(20022, 4), 79858, 35]-NRT-code)	[i]
4	Linear OOA(3²³⁰, 20022, F₃, 5, 34) (dual of [(20022, 5), 99880, 35]-NRT-code)	[i]
5	Digital (196, 230, 20022)-net over F₃	[i]