MinT - Information on Result #2486846

Information on Result #2486846

Linear OOA(3²⁰⁶, 265751, F₃, 2, 24) (dual of [(265751, 2), 531296, 25]-NRT-code), using 3¹ times duplication based on linear OOA(3²⁰⁵, 265751, F₃, 2, 24) (dual of [(265751, 2), 531297, 25]-NRT-code), using

strength reduction [i] based on linear OOA(3²⁰⁵, 265751, F₃, 2, 25) (dual of [(265751, 2), 531297, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3²⁰⁵, 531502, F₃, 25) (dual of [531502, 531297, 26]-code), using
  - 1 times code embedding in larger space [i] based on linear OA(3²⁰⁴, 531501, F₃, 25) (dual of [531501, 531297, 26]-code), using
    - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(3¹⁹³, 531442, F₃, 25) (dual of [531442, 531249, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
      2. linear OA(3¹⁴⁵, 531442, F₃, 19) (dual of [531442, 531297, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 3²⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(3¹¹, 59, F₃, 5) (dual of [59, 48, 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(3²⁰⁶, 187201, F₃, 3, 24) (dual of [(187201, 3), 561397, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²⁰⁶, 187201, F₃, 4, 24) (dual of [(187201, 4), 748598, 25]-NRT-code)	[i]
3	Linear OOA(3²⁰⁶, 187201, F₃, 5, 24) (dual of [(187201, 5), 935799, 25]-NRT-code)	[i]
4	Digital (182, 206, 187201)-net over F₃	[i]