MinT - Information on Result #2435768

Information on Result #2435768

Linear OOA(3²¹², 29550, F₃, 2, 30) (dual of [(29550, 2), 58888, 31]-NRT-code), using strength reduction based on linear OOA(3²¹², 29550, F₃, 2, 31) (dual of [(29550, 2), 58888, 32]-NRT-code), using

OOA 2-folding [i] based on linear OA(3²¹², 59100, F₃, 31) (dual of [59100, 58888, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(3²¹², 59101, F₃, 31) (dual of [59101, 58889, 32]-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(3¹¹, 51, F₃, 5) (dual of [51, 40, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹¹, 85, F₃, 5) (dual of [85, 74, 6]-code), using
        codes constructed by inverting constructionÂ Y₁ [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(3²¹², 28049, F₃, 3, 30) (dual of [(28049, 3), 83935, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²¹², 28049, F₃, 4, 30) (dual of [(28049, 4), 111984, 31]-NRT-code)	[i]
3	Linear OOA(3²¹², 28049, F₃, 5, 30) (dual of [(28049, 5), 140033, 31]-NRT-code)	[i]
4	Digital (182, 212, 28049)-net over F₃	[i]