MinT - Information on Result #814184

Information on Result #814184

Linear OOA(3¹⁸⁶, 88600, F₃, 2, 24) (dual of [(88600, 2), 177014, 25]-NRT-code), using OOA 2-folding based on linear OA(3¹⁸⁶, 177200, F₃, 24) (dual of [177200, 177014, 25]-code), using

discarding factors / shortening the dual code based on linear OA(3¹⁸⁶, 177201, F₃, 24) (dual of [177201, 177015, 25]-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(3⁹, 53, F₃, 4) (dual of [53, 44, 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(3¹⁸⁶, 65739, F₃, 3, 24) (dual of [(65739, 3), 197031, 25]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸⁶, 65739, F₃, 4, 24) (dual of [(65739, 4), 262770, 25]-NRT-code)	[i]
3	Linear OOA(3¹⁸⁶, 65739, F₃, 5, 24) (dual of [(65739, 5), 328509, 25]-NRT-code)	[i]
4	Digital (162, 186, 65739)-net over F₃	[i]