MinT - Information on Result #2677568

Information on Result #2677568

Linear OOA(3¹⁸⁶, 177156, F₃, 3, 23) (dual of [(177156, 3), 531282, 24]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁸⁵, 177156, F₃, 3, 23) (dual of [(177156, 3), 531283, 24]-NRT-code), using

OOA 3-folding [i] based on linear OA(3¹⁸⁵, 531468, F₃, 23) (dual of [531468, 531283, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(3¹⁸⁵, 531469, F₃, 23) (dual of [531469, 531284, 24]-code), using
  - constructionÂ X applied to C_e(22) âŠ‚ C_e(19) [i] based on
    1. linear OA(3¹⁸¹, 531441, F₃, 23) (dual of [531441, 531260, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    2. linear OA(3¹⁵⁷, 531441, F₃, 20) (dual of [531441, 531284, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
    3. linear OA(3⁴, 28, F₃, 2) (dual of [28, 24, 3]-code), using
      - discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
        Hamming code H(4,3) [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, 156159, F₃, 4, 23) (dual of [(156159, 4), 624450, 24]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹⁸⁶, 156159, F₃, 5, 23) (dual of [(156159, 5), 780609, 24]-NRT-code)	[i]
3	Digital (163, 186, 156159)-net over F₃	[i]