MinT - Information on Result #812717

Information on Result #812717

Linear OOA(3⁵⁵, 9846, F₃, 2, 9) (dual of [(9846, 2), 19637, 10]-NRT-code), using OOA 2-folding based on linear OA(3⁵⁵, 19692, F₃, 9) (dual of [19692, 19637, 10]-code), using

discarding factors / shortening the dual code based on linear OA(3⁵⁵, 19693, F₃, 9) (dual of [19693, 19638, 10]-code), using
- 1 times truncation [i] based on linear OA(3⁵⁶, 19694, F₃, 10) (dual of [19694, 19638, 11]-code), using
  - constructionÂ X4 applied to C_e(9) âŠ‚ C_e(7) [i] based on
    1. linear OA(3⁵⁵, 19683, F₃, 10) (dual of [19683, 19628, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [i]
    2. linear OA(3⁴⁶, 19683, F₃, 8) (dual of [19683, 19637, 9]-code), using an extension C_e(7) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 3⁹âˆ’1, defining interval IÂ =Â [1,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 8 [i]
    3. linear OA(3¹⁰, 11, F₃, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,3)), using
      - dual of repetition code with length 11 [i]
    4. linear OA(3¹, 11, F₃, 1) (dual of [11, 10, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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(3⁵⁵, 9846, F₃, 3, 9) (dual of [(9846, 3), 29483, 10]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(3⁵⁵, 9846, F₃, 4, 9) (dual of [(9846, 4), 39329, 10]-NRT-code)	[i]
3	Linear OOA(3⁵⁵, 9846, F₃, 5, 9) (dual of [(9846, 5), 49175, 10]-NRT-code)	[i]
4	Digital (46, 55, 9846)-net over F₃	[i]