MinT - Information on Result #2486631

Information on Result #2486631

Linear OOA(3¹³³, 9853, F₃, 2, 22) (dual of [(9853, 2), 19573, 23]-NRT-code), using 3¹ times duplication based on linear OOA(3¹³², 9853, F₃, 2, 22) (dual of [(9853, 2), 19574, 23]-NRT-code), using

OOA 2-folding [i] based on linear OA(3¹³², 19706, F₃, 22) (dual of [19706, 19574, 23]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3¹³¹, 19705, F₃, 22) (dual of [19705, 19574, 23]-code), using
  - constructionÂ X applied to C_e(21) âŠ‚ C_e(18) [i] based on
    1. linear OA(3¹²⁷, 19683, F₃, 22) (dual of [19683, 19556, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
    2. linear OA(3¹⁰⁹, 19683, F₃, 19) (dual of [19683, 19574, 20]-code), using an extension C_e(18) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,18], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [i]
    3. linear OA(3⁴, 22, F₃, 2) (dual of [22, 18, 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(3¹³³, 7705, F₃, 3, 22) (dual of [(7705, 3), 22982, 23]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3¹³³, 7705, F₃, 4, 22) (dual of [(7705, 4), 30687, 23]-NRT-code)	[i]
3	Linear OOA(3¹³³, 7705, F₃, 5, 22) (dual of [(7705, 5), 38392, 23]-NRT-code)	[i]
4	Digital (111, 133, 7705)-net over F₃	[i]