MinT - Information on Result #2434464

Information on Result #2434464

Linear OOA(3¹⁸⁸, 88601, F₃, 2, 24) (dual of [(88601, 2), 177014, 25]-NRT-code), using strength reduction based on linear OOA(3¹⁸⁸, 88601, F₃, 2, 25) (dual of [(88601, 2), 177014, 26]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹⁸⁸, 177202, F₃, 25) (dual of [177202, 177014, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁸⁸, 177203, F₃, 25) (dual of [177203, 177015, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,9]) [i] based on
    1. 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]
    2. linear OA(3¹³³, 177148, F₃, 19) (dual of [177148, 177015, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148Â | 3²²âˆ’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, 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(3¹⁸⁸, 72992, F₃, 3, 24) (dual of [(72992, 3), 218788, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸⁸, 72992, F₃, 4, 24) (dual of [(72992, 4), 291780, 25]-NRT-code)	[i]
3	Linear OOA(3¹⁸⁸, 72992, F₃, 5, 24) (dual of [(72992, 5), 364772, 25]-NRT-code)	[i]
4	Digital (164, 188, 72992)-net over F₃	[i]