MinT - Information on Result #815018

Information on Result #815018

Linear OOA(3²¹⁰, 29549, F₃, 2, 30) (dual of [(29549, 2), 58888, 31]-NRT-code), using OOA 2-folding based on linear OA(3²¹⁰, 59098, F₃, 30) (dual of [59098, 58888, 31]-code), using

discarding factors / shortening the dual code based on linear OA(3²¹⁰, 59099, F₃, 30) (dual of [59099, 58889, 31]-code), using
- constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
  1. linear OA(3²⁰¹, 59050, F₃, 31) (dual of [59050, 58849, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
  2. linear OA(3¹⁶¹, 59050, F₃, 25) (dual of [59050, 58889, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 59050Â | 3²⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
  3. linear OA(3⁹, 49, F₃, 4) (dual of [49, 40, 5]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁹, 80, F₃, 4) (dual of [80, 71, 5]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 80Â = 3⁴âˆ’1, defining interval IÂ =Â [0,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [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(3²¹⁰, 25855, F₃, 3, 30) (dual of [(25855, 3), 77355, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²¹⁰, 25855, F₃, 4, 30) (dual of [(25855, 4), 103210, 31]-NRT-code)	[i]
3	Linear OOA(3²¹⁰, 25855, F₃, 5, 30) (dual of [(25855, 5), 129065, 31]-NRT-code)	[i]
4	Digital (180, 210, 25855)-net over F₃	[i]