MinT - Information on Result #815030

Information on Result #815030

Linear OOA(3²³⁶, 88608, F₃, 2, 30) (dual of [(88608, 2), 176980, 31]-NRT-code), using OOA 2-folding based on linear OA(3²³⁶, 177216, F₃, 30) (dual of [177216, 176980, 31]-code), using

discarding factors / shortening the dual code based on linear OA(3²³⁶, 177217, F₃, 30) (dual of [177217, 176981, 31]-code), using
- 1 times truncation [i] based on linear OA(3²³⁷, 177218, F₃, 31) (dual of [177218, 176981, 32]-code), using
  - constructionÂ X applied to C_e(30) âŠ‚ C_e(22) [i] based on
    1. linear OA(3²²¹, 177147, F₃, 31) (dual of [177147, 176926, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
    2. linear OA(3¹⁶⁶, 177147, F₃, 23) (dual of [177147, 176981, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 177146Â = 3¹¹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
    3. linear OA(3¹⁶, 71, F₃, 7) (dual of [71, 55, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹⁶, 82, F₃, 7) (dual of [82, 66, 8]-code), using
        generator matrices provided on Edelâ€™s homepage [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(3²³⁶, 74521, F₃, 3, 30) (dual of [(74521, 3), 223327, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3²³⁶, 74521, F₃, 4, 30) (dual of [(74521, 4), 297848, 31]-NRT-code)	[i]
3	Linear OOA(3²³⁶, 74521, F₃, 5, 30) (dual of [(74521, 5), 372369, 31]-NRT-code)	[i]
4	Digital (206, 236, 74521)-net over F₃	[i]