MinT - Information on Result #2487405

Information on Result #2487405

Linear OOA(3²³⁵, 88603, F₃, 2, 30) (dual of [(88603, 2), 176971, 31]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(3²³¹, 88601, F₃, 2, 30) (dual of [(88601, 2), 176971, 31]-NRT-code), using

OOA 2-folding [i] based on linear OA(3²³¹, 177202, F₃, 30) (dual of [177202, 176971, 31]-code), using
- 1 times truncation [i] based on linear OA(3²³², 177203, F₃, 31) (dual of [177203, 176971, 32]-code), using
  - constructionÂ X applied to C([0,15]) âŠ‚ C([0,12]) [i] based on
    1. linear OA(3²²¹, 177148, F₃, 31) (dual of [177148, 176927, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
    2. linear OA(3¹⁷⁷, 177148, F₃, 25) (dual of [177148, 176971, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’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, 55, F₃, 5) (dual of [55, 44, 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(3²³⁵, 71548, F₃, 3, 30) (dual of [(71548, 3), 214409, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²³⁵, 71548, F₃, 4, 30) (dual of [(71548, 4), 285957, 31]-NRT-code)	[i]
3	Linear OOA(3²³⁵, 71548, F₃, 5, 30) (dual of [(71548, 5), 357505, 31]-NRT-code)	[i]
4	Digital (205, 235, 71548)-net over F₃	[i]